On fixed point free involutions of
Gerhard X. Ritter (1976)
Colloquium Mathematicae
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Gerhard X. Ritter (1976)
Colloquium Mathematicae
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Giulio Ciraolo, Rolando Magnanini, Shigeru Sakaguchi (2015)
Journal of the European Mathematical Society
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We consider the functional where is a bounded domain and is a convex function. Under general assumptions on , Crasta [Cr1] has shown that if admits a minimizer in depending only on the distance from the boundary of , then must be a ball. With some restrictions on , we prove that spherical symmetry can be obtained only by assuming that the minimizer has one level surface parallel to the boundary (i.e. it has only a level surface in common with the distance). We then discuss...
Rüdiger Göbel, Daniel Herden, Saharon Shelah (2014)
Journal of the European Mathematical Society
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It is a well-known fact that modules over a commutative ring in general cannot be classified, and it is also well-known that we have to impose severe restrictions on either the ring or on the class of modules to solve this problem. One of the restrictions on the modules comes from freeness assumptions which have been intensively studied in recent decades. Two interesting, distinct but typical examples are the papers by Blass [1] and Eklof [8], both jointly with Shelah. In the first case...
Carlo Greco (2017)
Commentationes Mathematicae Universitatis Carolinae
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In a cholesteric liquid crystal the director field tends to form a right-angle helicoid around a twist axis in order to minimize the internal energy; however, a fixed alignment of the director field at the boundary (strong anchoring) can give rise to distorted configurations of the director field, as oblique helicoid, in order to save energy. The transition to this distorted configurations depend on the boundary conditions and on the geometry of the liquid crystal, and it is known...
Martin Arkowitz, Mauricio Gutierrez (2002)
Fundamenta Mathematicae
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If f:G → H is a group homomorphism and p,q are the projections from the free product G*H onto its factors G and H respectively, let the group be the equalizer of fp and q:G*H → H. Then p restricts to an epimorphism . A right inverse (section) of is called a coaction on G. In this paper we study and the sections of . We consider the following topics: the structure of as a free product, the restrictions on G resulting from the existence of a coaction, maps of coactions and...
Yihong Du, Bendong Lou (2015)
Journal of the European Mathematical Society
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We study nonlinear diffusion problems of the form with free boundaries. Such problems may be used to describe the spreading of a biological or chemical species, with the free boundary representing the expanding front. For special of the Fisher-KPP type, the problem was investigated by Du and Lin [DL]. Here we consider much more general nonlinear terms. For any which is and satisfies , we show that the omega limit set of every bounded positive solution is determined by a stationary...
Svobodová, Ivona
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We consider functionals of a potential energy corresponding to . We are dealing with with . Various types of the subsoil of the plate are described by various types of the nonlinear term . The aim of the paper is to find a suitable computational algorithm.
Graziano Crasta (2006)
Journal of the European Mathematical Society
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We consider the integral functional , , where , , is a nonempty bounded connected open subset of with smooth boundary, and is a convex, differentiable function. We prove that if admits a minimizer in depending only on the distance from the boundary of , then must be a ball.
Per Åhag, Rafał Czyż, Pham Hoàng Hiêp (2007)
Annales Polonici Mathematici
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The energy class is studied for 0 < p < 1. A characterization of certain bounded plurisubharmonic functions in terms of and its pluricomplex p-energy is proved.
Nikolay Nikolov, László Pyber (2011)
Journal of the European Mathematical Society
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We first note that a result of Gowers on product-free sets in groups has an unexpected consequence: If is the minimal degree of a representation of the finite group , then for every subset of with we have . We use this to obtain improved versions of recent deep theorems of Helfgott and of Shalev concerning product decompositions of finite simple groups, with much simpler proofs. On the other hand, we prove a version of Jordan’s theorem which implies that if , then has a...
Michael Bildhauer, Martin Fuchs, Xiao Zhong (2007)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Starting from Giaquinta’s counterexample [12] we introduce the class of splitting functionals being of -growth with exponents and show for the scalar case that locally bounded local minimizers are of class . Note that to our knowledge the only -results without imposing a relation between and concern the case of two independent variables as it is outlined in Marcellini’s paper [15], Theorem A, and later on in the work of Fusco and Sbordone [10], Theorem 4.2.
Giovanni Alberti, S. Baldo, G. Orlandi (2003)
Journal of the European Mathematical Society
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The distributional -dimensional Jacobian of a map in the Sobolev space which takes values in the sphere can be viewed as the boundary of a rectifiable current of codimension carried by (part of) the singularity of which is topologically relevant. The main purpose of this paper is to investigate the range of the Jacobian operator; in particular, we show that any boundary of codimension can be realized as Jacobian of a Sobolev map valued in . In case is polyhedral, the...
Sichun Wang (2006)
Studia Mathematica
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Let d > 0 be a positive real number and n ≥ 1 a positive integer and define the operator and its associated global maximal operator by , f ∈ (ℝⁿ), x ∈ ℝⁿ, t ∈ ℝ, , f ∈ (ℝⁿ), x ∈ ℝⁿ, where f̂ is the Fourier transform of f and (ℝⁿ) is the Schwartz class of rapidly decreasing functions. If d = 2, is the solution to the initial value problem for the free Schrödinger equation (cf. (1.3) in this paper). We prove that for radial functions f ∈ (ℝⁿ), if n ≥ 3, 0 < d ≤ 2, and p ≥...
Arkady Poliakovsky (2007)
Journal of the European Mathematical Society
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We prove an upper bound for the Aviles–Giga problem, which involves the minimization of the energy over , where is a small parameter. Given such that and a.e., we construct a family satisfying: in and as goes to 0.
Marek Bożejko, Gero Fendler (2006)
Banach Center Publications
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We show that for the t-deformed semicircle measure, where 1/2 < t ≤ 1, the expansions of functions with respect to the associated orthonormal polynomials converge in norm when 3/2 < p < 3 and do not converge when 1 ≤ p < 3/2 or 3 < p. From this we conclude that natural expansions in the non-commutative spaces of free group factors and of free commutation relations do not converge for 1 ≤ p < 3/2 or 3 < p.
Zujin Zhang, Xian Yang (2016)
Colloquium Mathematicae
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We study the Cauchy problem for the 3D MHD system with damping terms and (ε, δ > 0 and α, β ≥ 1), and show that the strong solution exists globally for any α, β > 3. This improves the previous results significantly.
Alexander Ženíšek (1996)
Applications of Mathematics
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The finite element method for a strongly elliptic mixed boundary value problem is analyzed in the domain whose boundary is formed by two circles , with the same center and radii , , where . On one circle the homogeneous Dirichlet boundary condition and on the other one the nonhomogeneous Neumann boundary condition are prescribed. Both possibilities for are considered. The standard finite elements satisfying the minimum angle condition are in this case inconvenient; thus...
Stéphane Jaffard (2006)
Banach Center Publications
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The purpose of multifractal analysis of functions is to determine the Hausdorff dimensions of the sets of points where a function (or a distribution) f has a given pointwise regularity exponent H. This notion has many variants depending on the global hypotheses made on f; if f locally belongs to a Banach space E, then a family of pointwise regularity spaces are constructed, leading to a notion of pointwise regularity with respect to E; the case corresponds to the usual Hölder regularity,...