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Displaying 1501 –
1520 of
1784
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.
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...
Dans cette partie de la théorie des potentiels besseliens on considère les restrictions de potentiels de la classe aux domaines ouverts . On cherche à caractériser de manière intrinsèque la classe ainsi obtenue.On attaque ce problème en définissant de manière directe (§ 2) une classe qui, pour des domaines assez réguliers, est égale à .L’égalité est équivalente à l’existence d’un opérateur-extension , linéaire et continu, tel que soit une extension de . Si un tel opérateur transforme...
In this paper Bessel potentials on -Riemannian manifolds (open or bordered) are studied. Let be an -dimensional manifold, and a submanifold of of dimension . Sufficient conditions are given for: 1) the restriction to of any potential of order on to be a potential of order on ; 2) any potential of order on to be extendable to a potential of order on . It is also proved that for a bordered manifold the restriction to its interior is an isometric isomorphism between the...
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 we define the local potentials of reduced order, if for any chart of the structure of can be extended from to the whole of as potential in . This definition is not intrinsic. We obtain an intrinsic characterization of when is with singularities...
Let , denote the space of Bessel potentials , , with norm . For integer can be identified with the Sobolev space .One can associate a potential theory to these spaces much in the same way as classical potential theory is associated to the space , 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...
In this paper we outline some recent results concerning the existence of steady solutions to the Euler equation in with a prescribed set of (possibly knotted and linked) thin vortex tubes.
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. ) and equations of type.
Let be a domain of type in a Brelot potential theory. A compact in is a in iff has at most countably many components. If is a relatively closed locally polar subset of , any in is a in . If is a domain in , all Borel subsets of are Baire even if is not metrizable. The known results concerning equivalences between weak thinness, thinness, and strong thinness of a set at a point are extended from the case where is a to the cases in which meets only countably...
Nous commençons par définir la notion d’espaces où est une capacité, ce qui permet d’introduire la notion de mesure d’énergie finie par rapport à , et de parler d’espaces de Dirichlet basés sur .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).
On définit sur un espace vectoriel une classe de topologies qui rendent la multiplication continue, mais ne sont pas vectorielles en général. Sur un espace complexe 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...
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