Bounded Solutions for Some Dirichlet Problems with Data
Tommaso Leonori (2007)
Bollettino dell'Unione Matematica Italiana
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In this paper we prove the existence of a solution for a problem whose model is: with in and , .
Tommaso Leonori (2007)
Bollettino dell'Unione Matematica Italiana
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In this paper we prove the existence of a solution for a problem whose model is: with in and , .
Ezio Stagnaro (2007)
Bollettino dell'Unione Matematica Italiana
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Using the theory of adjoints and pluricanonical adjoints, we construct three nonsingular threefolds, as desingularizations of degree six hypersurfaces in , having the irregularities and the following periodical sequences of plurigenera respectively In the Appendix, starting from the second above-mentioned example, we construct a threefold of general type with , whose m-canonical transformation is birational if and only if .
Daniela Giachetti, François Murat (2009)
Bollettino dell'Unione Matematica Italiana
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We prove the existence of distributional solutions to an elliptic problem with a lower order term which depends on the solution in a singular way and on its gradient with quadratic growth. The prototype of the problem under consideration is where , ; , (and so ). If , we prove the existence of a solution for both the "+" and the "-" signs, while if , we prove the existence of a solution for the "+" sign only.
Gabriella Zecca (2007)
Bollettino dell'Unione Matematica Italiana
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Let us consider a Young's function satisfying the condition together with its complementary function , and let us consider the Dirichlet problem for a second order elliptic operator in divergence form: the unit ball of . In this paper we give a necessary and sufficient condition for the -solvability of the problem, where is the Orlicz Space generated by the function . This means solvability for in the sense of [5], [8], where the case is treated. ...
A. Azzollini, A. Pomponio (2009)
Bollettino dell'Unione Matematica Italiana
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In this paper we study the nonlinear Schrödinger-Maxwell equations If is a positive constant, we prove the existence of a ground state solution for . The non-constant potential case is treated for , and possibly unbounded below.
Piotr Słanina, Witold Tomaszewski (2007)
Bollettino dell'Unione Matematica Italiana
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We use notations: and e . We consider groups generated by , satisfying relations or , . We call groups of the first type mep-groups and of the second type nmep-groups. We show many properties and examples of mep- and nmep-groups. We prove that if is a prime then the group is a nmep-group. We give the necessary and sufficient conditions for metacyclic group to be a nmep-group and we show that nmep-groups with presentation are finite.
Marino Badiale, Vieri Benci, Sergio Rolando (2009)
Bollettino dell'Unione Matematica Italiana
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We prove the existence of rotating solitary waves (vortices) for the nonlinear Klein-Gordon equation with nonnegative potential, by finding nonnegative cylindrical solutions to the standing equation where , , and . The nonnegativity of the potential makes the equation suitable for physical models and guarantees the wellposedness of the corresponding Cauchy problem, but it prevents the use of standard arguments in providing the functional associated to with bounded Palais-Smale...
D.E. Edmunds, J. Lang (2008)
Bollettino dell'Unione Matematica Italiana
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Let , let , let and be positive functions with e and let be the Hardy-type operator given by We show that the asymptotic behavior of the eigenvaluesof the non-linear integral system (where, for example,is given by Here, is an explicit constant depending only on and , , where stands for the set of all eigenvalues corresponding to eigenfunctions with zeros.
Patrizia Di Gironimo (2007)
Bollettino dell'Unione Matematica Italiana
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In this paper we study the degree of integrability of quasiharmonic fields. These fields are connected with the study of the equation , where the symmetric matrix satisfies the condition .The nonnegative function belongs to the exponential class, i.e. is integrable for some . We prove that the gradient of a local solution of the equation belongs to the Zygmund spaces , . Moreover we show exactly how the degree of improved regularity depends on .
Mourad Sfaxi, Ali Sili (2007)
Bollettino dell'Unione Matematica Italiana
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We study the problem of correctors in the framework of the homogenization of linear parabolic equations posed in a heterogeneous medium made of two materials. The first one is located in a set of cylindrical parallel fibers periodically distributed with a period of size , and the second one is located in the "matrix" . The ratio between the conductivity coefficients of the two materials is of order . After writing the homogenized problem, we give a corrector result and prove...
Teresa Radice, Eero Saksman, Gabriella Zecca (2009)
Bollettino dell'Unione Matematica Italiana
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Let and be the unit circle and the unit disc in the plane and let us denote by the algebra of the complex-valued continuous functions on which are traces of functions in the Sobolev class . On we define the following norm where is the harmonic extension of to . We prove that every isomorphism of the functional algebra is a quasitsymmetric change of variables on .
Daniel D. Anderson, Muhammad Zafrullah (2007)
Bollettino dell'Unione Matematica Italiana
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Let be an integral domain with quotient field . Recall that is Schreier if is integrally closed and for all , implies that where e . A GCD domain is Schreier. We show that an integral domain is a GCD domain if and only if (i) for each pair , there is a finitely generated ideal such that and (ii) every quadratic in that is a product of two linear polynomials in is a product of two linear polynomials in . We also show that is Schreier if and only if every...
Daniele Graziani (2007)
Bollettino dell'Unione Matematica Italiana
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The aim of this work is to prove a chain rule and an -lower semicontinuity theorems for integral functional defined on . Moreover we apply this result in order to obtain new relaxation and -convergence result without any coerciveness and any continuity assumption of the integrand with respect to the variable .
Francesco Borrello (2007)
Bollettino dell'Unione Matematica Italiana
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In this paper we study local regularity for the generalized solution to the Dirichlet problem related to the equation where are vector fields satisfying Hörmander condition and . We give a representation formula for the generalized solution in terms of the Green function and thanks to suitable estimates we achieve our goal. In the case we are able to give necessary condition too.
Francesca Prinari (2006)
Bollettino dell'Unione Matematica Italiana
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We prove that the -limit in of a sequence of supremal functionals of the form is itself a supremal functional. We show by a counterexample that, in general, the function which represents the -lim of a sequence of functionals can depend on the set and wegive a necessary and sufficient condition to represent in the supremal form. As a corollary, if represents a supremal functional, then the level convex envelope of represents its weak* lower semicontinuous envelope. ...
Giuseppe Da Prato, Luciano Tubaro (2008)
Bollettino dell'Unione Matematica Italiana
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We consider an SPDE in a Hilbert space of the form , and the corresponding transition semigroup . We define the infinitesimal generator of through the Laplace transform of as in [1]. Then we consider the differential operator defined on a suitable set of regular functions. Our main result is that if is a core for , then there exists a unique solution of the martingale problem defined in terms of . Application to the Ornstein-Uhlenbeck equation and to some regular...
Lucia Marino (2006)
Bollettino dell'Unione Matematica Italiana
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We attempt to generalize conductor degree's results, known in , to the case of 0-dimensional schemes of . In the first part of this paper, we consider the problem of characterizing the sequences generators's degrees of the conductor which are compatible with a fixed postulation (or Hilbert function) for a set of points in and we determine the conductor degree of every point in a -partial intersection. In addition, we define the separating degree of a point for a 0-dimensional subscheme...
Nowak Grzegorz (2006)
Bollettino dell'Unione Matematica Italiana
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We consider the Kantorovich and the Durrmeyer type modifications of the generalized Favard operators and we prove inverse approximation theorems for functions such that , where and , .
Miriam Ciavarella (2006)
Bollettino dell'Unione Matematica Italiana
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The object of this note is to study certain 2-dimensional -adic representations of ; fixed distinct primes, we will consider representations , given by the matrix which are unramified outside and the residue characteristic of , which are a product of representations over finite extensions of the ring of Witt vectors of the residue field and which are reducible modulo . In analogy with the theory of the modular representations, we will introduce the analogue of Mazur's Hecke...
Daniele Faenzi (2006)
Bollettino dell'Unione Matematica Italiana
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The Tango bundle is defined as the pull-back of the Cayley bundle over a smooth quadric in via a map existing only in characteristic 2 and factorizing the Frobenius . The cohomology of is computed in terms of , , and , which we handle with Borel-Bott-Weil theorem.
Pietro Sabatino (2006)
Bollettino dell'Unione Matematica Italiana
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Let be a smooth irreducible non degenerate surface over the complex numbers, . We define the projective genus of , denoted by , as the geometric genus of the singular curve of the projection of from a general linear subspace of codimension four. Denote by the sectional genus of . In this paper we conjecture that the only surfaces for which are the del Pezzo surface in , in and a conic bundle of degree 5 in . We prove that for if , a non negative integer, then where...
Marilena Massa (2007)
Bollettino dell'Unione Matematica Italiana
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We study the irreducibility of the Dirichlet polynomial when is the alternating group on elements with prime and we prove that is irreducible for infinitely many choiches of .
D. Cruz-Uribe, L. Diening, A. Fiorenza (2009)
Bollettino dell'Unione Matematica Italiana
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We give a new proof using the classic Calderón-Zygmund decomposition that the Hardy-Littlewood maximal operator is bounded on the variable Lebesgue space whenever the exponent function satisfies log-Hölder continuity conditions. We include the case where assumes the value infinity. The same proof also shows that the fractional maximal operator , , maps into , where .
R. Supper (2009)
Bollettino dell'Unione Matematica Italiana
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This article is devoted to sequences of subharmonic functions in , with finite order, whose means (over spheres centered at the origin, with radius r) satisfy such a condition as: , such that , . The paper investigates under which conditions one may extract a pointwise or uniformly convergent subsequence.
Andrija Raguž (2007)
Bollettino dell'Unione Matematica Italiana
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In this note we consider the Ginzburg-Landau functional where and a is 1-periodic. We determine how (rescaled) minimal asymptotic energy associated to depends on parameter as . In particular, our analysis shows that minimizers of are nearly -periodic.
Miriam Ciavarella (2006)
Bollettino dell'Unione Matematica Italiana
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We fix a prime and let be an integer such that ; let be a newform supercuspidal of fixed type at and special at a finite set of primes. For an indefinite quaternion algebra over , of discriminant dividing the level of , there is a local quaternionic Hecke algebra associated to . The algebra acts on a module coming from the cohomology of a Shimura curve. Applying the Taylor-Wiles criterion and a recent Savitt's theorem, is the universal deformation ring of a global...
Horst Alzer (2009)
Bollettino dell'Unione Matematica Italiana
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Let We prove that is completely monotonic on . This complements a result of Miller and Moskowitz (2006), who proved that is positive and strictly decreasing on . The sequence plays a role in information theory.
Giuliano Parigi (2007)
Bollettino dell'Unione Matematica Italiana
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The aims of the present paper can be described as follows: a) In [2] Beauville showed that if some endomorphism a Jacobian has connected kernel, the principal polarization on induces a multiple of the principal polarization on the image of . We reformulate and complete this theorem proving "constructively" the following: Theorem. Let be an abelian subvariety and its complementary variety. is a Prym-Tyurin variety with respect to if and only if the following sequence...
Silvano Delladio (2007)
Bollettino dell'Unione Matematica Italiana
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Let be a couple of Lipschitz maps such that almost everywhere in . Then is a -rectifiable set, namely it may be covered by countably many curves of class embedded in . As a conseguence, projecting the rectifiable carrier of a one-dimensional generalized Gauss graph provides a -rectifiable set.
Costantino Capozzoli (2009)
Bollettino dell'Unione Matematica Italiana
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Assume that , are planar domains and is a homeomorphism belonging to Sobolev space with finite distortion. We prove that if the distortion function of satisfies the condition , then the distortion function of belongs to . We show that this result is sharp in sense that the conclusion fails if . Moreover, we prove that if the distortion function satisfies the condition for some , then belongs to for every . As special case of this result we show that if...
Eugenio Regazzini (2009)
Bollettino dell'Unione Matematica Italiana
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Let be the probability density function representing the solution of Kac's Boltzmann-like equation at time , with initial data , and let be the Gaussian density with zero mean and variance , being the value of the second moment of . Henry McKean Jr. put forward the conjecture that the total variation distance between and goes to zero, as , with an exponential rate equal to . This lecture aims at explaining the main efforts made to a view to validating this conjecture,...
D. Sivaraj, V. Renuka Devi (2007)
Bollettino dell'Unione Matematica Italiana
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We introduce a new class of spaces, called Hausdorff modulo or mod spaces with respect to an ideal which contains the class of all Hausdorff spaces. Characterizations of these spaces are given and their properties are investigated. The concept of compactness modulo an ideal was introduced by Newcomb in 1967 and studied by Hamlett and Jankovic in 1990. We study the properties of -compact subsets in Hausdorff modulo spaces and generalize some results of Hamlett and Jankovic....
Ralph Chill, Sachi Srivastava (2008)
Bollettino dell'Unione Matematica Italiana
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If the second order problem has maximal regularity for some , then it has maximal regularity for every .
Maddalena Bonanzinga, Filippo Cammaroto, Bruno A. Pansera (2007)
Bollettino dell'Unione Matematica Italiana
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In this note we show a relative version of -set introduced and studied in [12]. We give several characterizations of this property; in particular one of the characterizations is Ramsey theoretical. Also we give a result involving a property of the corresponding mapping between function spaces.
Giovanna Ilardi, Paola Supino, Jean Vallès (2009)
Bollettino dell'Unione Matematica Italiana
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We consider the Grassmannian of -dimensional linear subspaces of . We define as the classifying space of the -dimensional linear systems of degree on , whose bases realize a fixed number of polynomial relations of fixed degree , say syzygies of degree . Firstly, we compute the dimension of . In the second part we make a link between and the Poncelet varieties. In particular, we prove that the existence of linear syzygies implies the existence of singularities on the...
Giuseppe Caristi, Giovanni Molica Bisci (2007)
Bollettino dell'Unione Matematica Italiana
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In this paper we consider a random variable arising from an intersection problem between a fixed convex body and a system of random independent and uniformly distributed ovaloids in .
Alberto Venni (2008)
Bollettino dell'Unione Matematica Italiana
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The following results are proved: (i) if , and is a sectorial operator, then the set is bounded; (ii) the same set of operators is R-bounded if is R-sectorial.
Paolo Acquistapace, Brunello Terreni (1984)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti
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Si studiano esistenza, unicità e regolarità delle soluzioni strette, classiche e forti dell'equazione di evoluzione non autonoma con il dato iniziale , in uno spazio di Banach . Gli operatori sono generatori infinitesimali di semi-gruppi analitici ed hanno dominio indipendente da e non necessariamente denso in . Si danno condizioni necessarie e sufficienti per l'esistenza e la regolarità hölderiana della soluzione e della sua derivata.
Zbigniew Duszyński (2007)
Bollettino dell'Unione Matematica Italiana
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Richness of the class of -maps [3] is investigated. Several consequences for the theory of quasi--closed spaces are indicated.
Paolo Acquistapace, Brunello Terreni (1984)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
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Si studiano esistenza, unicità e regolarità delle soluzioni strette, classiche e forti dell'equazione di evoluzione non autonoma con il dato iniziale , in uno spazio di Banach . Gli operatori sono generatori infinitesimali di semi-gruppi analitici ed hanno dominio indipendente da e non necessariamente denso in . Si danno condizioni necessarie e sufficienti per l'esistenza e la regolarità hölderiana della soluzione e della sua derivata.
Angelo Alvino, Anna Mercaldo (2008)
Bollettino dell'Unione Matematica Italiana
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We consider the homogeneous Dirichlet problem for nonlinear elliptic equations as where is a measure with bounded total variation. We fix structural conditions on functions , which ensure existence of solutions. Moreover, if is an function, we prove a uniqueness result under more restrictive hypotheses on the operator.
Vittoria Bonanzinga, Loredana Sorrenti (2008)
Bollettino dell'Unione Matematica Italiana
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In this paper we determine all squarefree completely lexsegment ideals which have a linear resolution. Let denote the set of all squarefree monomials of degree in a polynomial ring in variables over a field . We order the monomials lexicographically such that , thus a lexsegment (of degree ) is a subset of of the form for some con . An ideal generated by a lexsegment is called a lexsegment ideal. We describe the procedure to determine when such an ideal has a linear...
M. Cristina Ronconi (2009)
Bollettino dell'Unione Matematica Italiana
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The range of the bigenus is one of the unsolved problems concerning smooth complex projective regular threefolds of general type with : The examples in the literature have . In the present paper we present a non-singular threefold with ; ; the bicanonical map is stably birational.
Gianni Dal Maso (1983)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti
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Se il problema di minimo è il limite, in senso variazionale, di una successione di problemi di minimo con ostacoli del tipo allora può essere scritto nella forma dove è un conveniente rappresentante di e è una misura non negativa.
Cristodor Ionescu, Gaetana Restuccia, Rosanna Utano (2007)
Bollettino dell'Unione Matematica Italiana
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Let be a finitely generated -module, having finite projective dimension. We study the acyclicity of the approximation complex of in terms of certain Fitting conditions on the Fitting ideals of the -th module of a projective resolution of . We deduce some good properties of the symmetric algebra of .
J. C. Rosales (2006)
Bollettino dell'Unione Matematica Italiana
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If is a pseudo-symmetric numerical semigroup, is its Frobenius number and is a minimal generator of , then , S and are also numerical semigroups. In this paper we study these constructions.
Giovanni Fiorito (2006)
Bollettino dell'Unione Matematica Italiana
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In this paper we give a recursive formula for the sequence of primes and apply it to find a necessary and sufficient condition in order that a prime number is equal to . Applications of previous results are given to evaluate the probability that is of the form ; moreover we prove that the limit of this probability is equal to zero as goes to . Finally, for every prime we construct a sequence whose terms that are in the interval are the first terms of two twin primes. This...