The Neumann eigenvalue problem for the $\infty$-Laplacian

B. Kawohl; C. Nitsch; C. Trombetti; L. Esposito

REVIEW

The Neumann eigenvalue problem for the infty-Laplacian

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 1405.3535 v2 pith:YWTPVFMG submitted 2014-05-14 math.AP

The Neumann eigenvalue problem for the $\infty$-Laplacian

L. Esposito , B. Kawohl , C. Nitsch , C. Trombetti This is my paper

classification math.AP

keywords eigenvaluelaplacianprobleminftyfirstneumannanaloguesconsequences

verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

0 comments

Share X Bluesky LinkedIn Reddit HN

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.

The Neumann eigenvalue problem for the $\infty$-Laplacian

discussion (0)