Abstract. — The first nontrivial eigenfunction of the Neumann eigenvalue problem for the p-Laplacian, suitably normalized, converges to a viscosity solution of an eigenvalue problem for the l-Laplacian as p ! l. We show among other things that the limiting eigenvalue, at least for convex sets, is in fact the first nonzero eigenvalue of the limiting problem. We then derive a number of consequences, which are nonlinear analogues of well-known inequalities for the linear (2-)Laplacian.
The Neumann eigenvalue problem for the ∞-Laplacian
ESPOSITO, Luca;
2015
Abstract
Abstract. — The first nontrivial eigenfunction of the Neumann eigenvalue problem for the p-Laplacian, suitably normalized, converges to a viscosity solution of an eigenvalue problem for the l-Laplacian as p ! l. We show among other things that the limiting eigenvalue, at least for convex sets, is in fact the first nonzero eigenvalue of the limiting problem. We then derive a number of consequences, which are nonlinear analogues of well-known inequalities for the linear (2-)Laplacian.File in questo prodotto:
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