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Strong boundary values : independence of the defining function and spaces of test functions

Jean-Pierre Rosay, Edgar Lee Stout (2002)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

The notion of “strong boundary values” was introduced by the authors in the local theory of hyperfunction boundary values (boundary values of functions with unrestricted growth, not necessarily solutions of a PDE). In this paper two points are clarified, at least in the global setting (compact boundaries): independence with respect to the defining function that defines the boundary, and the spaces of test functions to be used. The proofs rely crucially on simple results in spectral asymptotics.

Various kinds of sensitive singular perturbations

Nicolas Meunier, Jacqueline Sanchez-Hubert, Évariste Sanchez-Palencia (2007)

Annales mathématiques Blaise Pascal

We consider variational problems of P. D. E. depending on a small parameter ε when the limit process ε ↓ 0 implies vanishing of the higher order terms. The perturbation problem is said to be sensitive when the energy space of the limit problem is out of the distribution space, so that the limit problem is out of classical theory of P. D. E. We present here a review of the subject, including abstract convergence theorems and two very different model problems (the second one is presented for the first...

Currently displaying 41 – 60 of 70