The uniform norming of retractions on short intervals for certain function spaces.
The theory of Markov processes and the analysis on Lie groups are used to study the eigenvalue asymptotics of Dirichlet forms perturbed by scalar potentials.
The spatial gradient of solutions to non-homogeneous and degenerate parabolic equations of -Laplacean type can be pointwise estimated by natural Wolff potentials of the right hand side measure.
It is shown that the methods developed in an earlier paper of the author about a Dirichlet problem for the Silov boundary [Annales Inst. Fourier, 11 (1961)] lead in a new and natural way to the most important results about the convergence of positive linear operators on spaces of continuous functions defined on a compact space. Choquet’s notion of an adapted space of continuous functions in connection with results of Mokobodzki-Sibony opens the possibility of extending these results to the case...
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.
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.