Symmetrization of functions and principal eigenvalues of elliptic operators

François Hamel; Nikolai Nadirashvili; Emmanuel Russ

Displaying similar documents to “Symmetrization of functions and principal eigenvalues of elliptic operators”

Super and subsolutions for elliptic equations on all of $ℝ^{n}$ .

Afrouzi, G. A., Ghasemzadeh, H. (2002)

International Journal of Mathematics and Mathematical Sciences

Similarity:

Supercritical elliptic problems in domains with small holes

Manuel del Pino, Juncheng Wei (2007)

Annales de l'I.H.P. Analyse non linéaire

Similarity:

Picone's identity and the moving plane procedure.

Allegretto, Walter, Siegel, David (1995)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Similarity:

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

Similarity:

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.

Existence and perturbation of principal eigenvalues for a periodic-parabolic problem.

Daners, Daniel (2000)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Similarity:

Eigenvalues of the $p$ -Laplacian in $𝐑^{N}$ with indefinite weight

Yin Xi Huang (1995)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

We consider the nonlinear eigenvalue problem $- {div (| \nabla u |}^{p - 2} {\nabla u) = λ g (x) | u |}^{p - 2} u$ in $𝐑^{N}$ with $p > 1$ . A condition on indefinite weight function $g$ is given so that the problem has a sequence of eigenvalues tending to infinity with decaying eigenfunctions in $W^{1, p} (𝐑^{N})$ . A nonexistence result is also given for the case $p \geq N$ .

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

Parini, Enea (2010)

International Journal of Differential Equations

Similarity:

Displaying similar documents to “Symmetrization of functions and principal eigenvalues of elliptic operators”

Super and subsolutions for elliptic equations on all of ℝ n .

Supercritical elliptic problems in domains with small holes

Picone's identity and the moving plane procedure.

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

Existence and perturbation of principal eigenvalues for a periodic-parabolic problem.

Eigenvalues of the p -Laplacian in 𝐑 N with indefinite weight

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

Super and subsolutions for elliptic equations on all of $ℝ^{n}$ .

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

Eigenvalues of the $p$ -Laplacian in $𝐑^{N}$ with indefinite weight

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