Overdetermined problems and the -Laplacian.
Kawohl, Bernd (2007)
Acta Mathematica Universitatis Comenianae. New Series
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Kawohl, Bernd (2007)
Acta Mathematica Universitatis Comenianae. New Series
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Pierre Guerini, Alessandro Savo (2002-2003)
Séminaire de théorie spectrale et géométrie
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François Hamel, Nikolai Nadirashvili, Emmanuel Russ (2011-2012)
Séminaire Laurent Schwartz — EDP et applications
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In this paper, we consider shape optimization problems for the principal eigenvalues of second order uniformly elliptic operators in bounded domains of . We first recall the classical Rayleigh-Faber-Krahn problem, that is the minimization of the principal eigenvalue of the Dirichlet Laplacian in a domain with fixed Lebesgue measure. We then consider the case of the Laplacian with a bounded drift, that is the operator , for which the minimization problem is still well posed. Next, we...
Martínez, Sandra, Rossi, Julio D. (2002)
Abstract and Applied Analysis
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Kawohl, B.
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Lucio Damascelli (2000)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
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We present a simple proof of the fact that if is a bounded domain in , , which is convex and symmetric with respect to orthogonal directions, , then the nodal sets of the eigenfunctions of the laplacian corresponding to the eigenvalues must intersect the boundary. This result was proved by Payne in the case for the second eigenfunction, and by other authors in the case of convex domains in the plane, again for the second eigenfunction.
Manuel del Pino, Juncheng Wei (2007)
Annales de l'I.H.P. Analyse non linéaire
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