We study the dependence of the first eigenvalue of the $p$-Laplacian upon the variation of the domain: we prove a differentiability result and we find a Hadamard-type formula. Finally, we indicate how this formula yields a class of overdetermined nonlinear eigenvalue problems.
A DIFFERENTIABILITY RESULT FOR THE FIRST EIGENVALUE OF THE P-LAPLACIAN UPON DOMAIN PERTURBATION
LAMBERTI, PIER DOMENICO
2003
Abstract
We study the dependence of the first eigenvalue of the $p$-Laplacian upon the variation of the domain: we prove a differentiability result and we find a Hadamard-type formula. Finally, we indicate how this formula yields a class of overdetermined nonlinear eigenvalue problems.
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