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Schiffer problem and isoparametric hypersurfaces.

Vladimir E. Shklover (2000)

Revista Matemática Iberoamericana

The Schiffer Problem as originally stated for Euclidean spaces (and later for some symmetric spaces) is the following: Given a bounded connected open set Ω with a regular boundary and such that the complement of its closure is connected, does the existence of a solution to the Overdetermined Neumann Problem (N) imply that Ω is a ball? The same question for the Overdetermined Dirichlet Problem (D). We consider the generalization of the Schiffer problem to an arbitrary Riemannian manifold and also...

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.

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