The Neumann eigenvalue problem for the \(\infty\)-Laplacian

DOI10.4171/RLM/697zbMATH Open1321.35120arXiv1405.3535MaRDI QIDQ2354076

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Publication date: 10 July 2015

Published in: (Search for Journal in Brave)

Abstract: The first nontrivial eigenfunction of the Neumann eigenvalue problem for the $p$-Laplacian, suitable normalized, converges as $p$ goes to $infty$ to a viscosity solution of an eigenvalue problem for the $infty$-Laplacian. We show among other things that the limit of the 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.

Full work available at URL: https://arxiv.org/abs/1405.3535

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