The second eigenvalue of the -Laplacian as  goes to 1.

Parini, Enea

Displaying similar documents to “The second eigenvalue of the $p$ -Laplacian as $p$ goes to 1.”

Overdetermined problems and the $p$ -Laplacian.

Kawohl, Bernd (2007)

Acta Mathematica Universitatis Comenianae. New Series

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The Hodge laplacian on manifolds with boundary

Pierre Guerini, Alessandro Savo (2002-2003)

Séminaire de théorie spectrale et géométrie

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Symmetrization of functions and principal eigenvalues of elliptic operators

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 $ℝ^{n}$ . 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 $- Δ + v \cdot \nabla$ , for which the minimization problem is still well posed. Next, we...

Isolation and simplicity for the first eigenvalue of the $p$ -Laplacian with a nonlinear boundary condition.

Martínez, Sandra, Rossi, Julio D. (2002)

Abstract and Applied Analysis

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Overdetermined problems and the $p$ -Laplacian

Kawohl, B.

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On the nodal set of the second eigenfunction of the laplacian in symmetric domains in $R^{N}$

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 $Ω$ is a bounded domain in $R^{N}$ , $N \geq 2$ , which is convex and symmetric with respect to $k$ orthogonal directions, $1 \leq k \leq N$ , then the nodal sets of the eigenfunctions of the laplacian corresponding to the eigenvalues $λ_{2}, \dots, λ_{k + 1}$ must intersect the boundary. This result was proved by Payne in the case $N = 2$ for the second eigenfunction, and by other authors in the case of convex domains in the plane, again for the second eigenfunction.

Displaying similar documents to “The second eigenvalue of the p -Laplacian as p goes to 1.”

Overdetermined problems and the p -Laplacian.

The Hodge laplacian on manifolds with boundary

Symmetrization of functions and principal eigenvalues of elliptic operators

Isolation and simplicity for the first eigenvalue of the p -Laplacian with a nonlinear boundary condition.

Overdetermined problems and the p -Laplacian

On the nodal set of the second eigenfunction of the laplacian in symmetric domains in R N

Displaying similar documents to “The second eigenvalue of the $p$ -Laplacian as $p$ goes to 1.”

Overdetermined problems and the $p$ -Laplacian.

Isolation and simplicity for the first eigenvalue of the $p$ -Laplacian with a nonlinear boundary condition.

Overdetermined problems and the $p$ -Laplacian

On the nodal set of the second eigenfunction of the laplacian in symmetric domains in $R^{N}$