First eigenfunctions of the 1-Laplacian are viscosity solutions

Bernd Kawohl; Friedemann Schuricht

doi:10.3934/cpaa.2015.14.329

Article Contents

2015, Volume 14, Issue 1: 329-339. Doi: 10.3934/cpaa.2015.14.329

This issue Previous Article Nonuniqueness in vector-valued calculus of variations in $L^\infty$ and some Linear elliptic systems Next Article Some properties of minimizers of a variational problem involving the total variation functional

First eigenfunctions of the 1-Laplacian are viscosity solutions

Bernd Kawohl^1, and
Friedemann Schuricht^2,

1.
Mathematisches Institut, Universität zu Köln, 50923 Köln
2.
Fachrichtung Mathematik, Technische Universität Dresden,01062 Dresden

Received: January 31, 2014

Revised: February 28, 2014

Published: December 2014

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Abstract

We address the question if eigenfunctions of the 1-Laplacian, which are obtained through a variational argument, are also viscosity solutions of the associated strongly degenerate formal Euler equation. The answer is positive, but examples show also that there are many more viscosity solutions than expected.

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Mathematics Subject Classification: Primary: 35D40, 35J70, 49G05, 49A52.

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