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Displaying 1501 – 1520 of 1784

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Theoretical and numerical study of a free boundary problem by boundary integral methods

Michel Crouzeix, Philippe Féat, Francisco-Javier Sayas (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

In this paper we study a free boundary problem appearing in electromagnetism and its numerical approximation by means of boundary integral methods. Once the problem is written in a equivalent integro-differential form, with the arc parametrization of the boundary as unknown, we analyse it in this new setting. Then we consider Galerkin and collocation methods with trigonometric polynomial and spline curves as approximate solutions.

Theoretical aspects and numerical computation of the time-harmonic Green's function for an isotropic elastic half-plane with an impedance boundary condition

Mario Durán, Eduardo Godoy, Jean-Claude Nédélec (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

This work presents an effective and accurate method for determining, from a theoretical and computational point of view, the time-harmonic Green's function of an isotropic elastic half-plane where an impedance boundary condition is considered. This method, based on the previous work done by Durán et al. (cf. [Numer. Math.107 (2007) 295–314; IMA J. Appl. Math.71 (2006) 853–876]) for the Helmholtz equation in a half-plane, combines appropriately analytical and numerical techniques, which has an important...

Theory of Bessel potentials. II

Robert Adams, Nachman Aronszajn, K. T. Smith (1967)

Annales de l'institut Fourier

Dans cette partie de la théorie des potentiels besseliens on considère les restrictions de potentiels de la classe P a ( R n ) aux domaines ouverts D R n . On cherche à caractériser de manière intrinsèque la classe P a ( D ) ainsi obtenue.On attaque ce problème en définissant de manière directe (§ 2) une classe P ˇ a ( D ) P a ( D ) qui, pour des domaines assez réguliers, est égale à P a ( D ) .L’égalité P a ( D ) = P a ( D ) est équivalente à l’existence d’un opérateur-extension E : P ˇ a ( D ) P a ( R n ) , linéaire et continu, tel que E u soit une extension de u . Si un tel opérateur E transforme...

Theory of Bessel potentials. III : potentials on regular manifolds

Robert Adams, Nachman Aronszajn, M. S. Hanna (1969)

Annales de l'institut Fourier

In this paper Bessel potentials on C -Riemannian manifolds (open or bordered) are studied. Let M be an n -dimensional manifold, and N a submanifold of M of dimension k . Sufficient conditions are given for: 1) the restriction to N of any potential of order α on M to be a potential of order α - n - k 2 on N  ; 2) any potential of order α - n - k 2 on N to be extendable to a potential of order α on M . It is also proved that for a bordered manifold M the restriction to its interior M i is an isometric isomorphism between the...

Theory of Bessel potentials. IV. Potentials on subcartesian spaces with singularities of polyhedral type

Nachman Aronszajn, Pawel Szeptycki (1975)

Annales de l'institut Fourier

In the previous parts of the series on Bessel potentials the present part was announced as dealing with manifolds with singularities. The last notion is best defined in the more general framework of subcartesian spaces. In a subcartesian space X we define the local potentials of reduced order α : u P loc α ( X ) , if for any chart ( U , φ , R n ) of the structure of X , u γ - 1 can be extended from φ ( U ) to the whole of R n as potential in P loc α + ( n / 2 ) ( R n ) . This definition is not intrinsic. We obtain an intrinsic characterization of P loc α ( X ) when X is with singularities...

Thin sets in nonlinear potential theory

Lars-Inge Hedberg, Thomas H. Wolff (1983)

Annales de l'institut Fourier

Let L α q ( R D ) , α > 0 , 1 < q < , denote the space of Bessel potentials f = G α * g , g L q , with norm f α , q = g q . For α integer L α q can be identified with the Sobolev space H α , q .One can associate a potential theory to these spaces much in the same way as classical potential theory is associated to the space H 1 ; 2 , and a considerable part of the theory was carried over to this more general context around 1970. There were difficulties extending the theory of thin sets, however. By means of a new inequality, which characterizes the positive cone in the space...

Thin vortex tubes in the stationary Euler equation

Alberto Enciso, Daniel Peralta-Salas (2013)

Journées Équations aux dérivées partielles

In this paper we outline some recent results concerning the existence of steady solutions to the Euler equation in 3 with a prescribed set of (possibly knotted and linked) thin vortex tubes.

Thinness and non-tangential limit associated to coupled PDE

Allami Benyaiche, Salma Ghiate (2013)

Commentationes Mathematicae Universitatis Carolinae

In this paper, we study the reduit, the thinness and the non-tangential limit associated to a harmonic structure given by coupled partial differential equations. In particular, we obtain such results for biharmonic equation (i.e. 2 ϕ = 0 ) and equations of 2 ϕ = ϕ type.

Topological countability in Brelot potential theory

Thomas E. Armstrong (1974)

Annales de l'institut Fourier

Let U be a domain of type H in a Brelot potential theory. A compact K in U is a G δ in U iff U - K has at most countably many components. If F is a relatively closed locally polar subset of U , any G δ in F is a G δ in U . If V is a domain in U , all Borel subsets of V U are Baire even if V U is not metrizable. The known results concerning equivalences between weak thinness, thinness, and strong thinness of a set A at a point x A are extended from the case where { x } is a G δ to the cases in which A meets only countably...

Topologies fines et compactifications associées à certains espaces de Dirichlet

Denis Feyel, A. de La Pradelle (1977)

Annales de l'institut Fourier

Nous commençons par définir la notion d’espaces L 1 ( γ ) γ est une capacité, ce qui permet d’introduire la notion de mesure d’énergie finie par rapport à γ , et de parler d’espaces de Dirichlet basés sur γ .Soit d’autre part un espace de Dirichlet en ce sens avec potentiels s.c.i. : on étudie les espaces de Dirichlet sur les ouverts fins correspondants à l’aide d’une compactification. On retrouve plus facilement et on généralise les résultats de D. Feyel et A. de La Pradelle, (Lecture Notes).

Topologies semi-vectorielles. Application à l'analyse complexe

Pierre Lelong (1975)

Annales de l'institut Fourier

On définit sur un espace vectoriel E une classe de topologies qui rendent la multiplication continue, mais ne sont pas vectorielles en général. Sur un espace complexe E elles permettent d’obtenir encore les principales propriétés des fonctions plurisousharmoniques. De telles topologies séparées sont localement pseudo-convexes (mais non localement convexes en général) : cette notion intervient dans les extensions données récemment par l’auteur du théorème de Banach-Steinhaus aux familles de polynômes...

Currently displaying 1501 – 1520 of 1784