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.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11386/4658753
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