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Journal of Convex Analysis 15 (2008), No. 3, 623--634
Copyright Heldermann Verlag 2008

The p-Laplace Eigenvalue Problem as p Approaches 1 and Cheeger Sets in a Finsler Metric

Bernd Kawohl
Mathematisches Institut, Universitaet Koeln, 50923 Koeln, Germany

Matteo Novaga
Dip. di Matematica, UniversitÓ di Pisa, Largo B. Pontecorvo 5, 56127 Pisa, Italy


We consider the $p$-Laplacian operator on a domain equipped with a Finsler metric. After deriving and recalling relevant properties of its first eigenfunction for $p>1$, we investigate the limit problem as $p\to 1$.

Keywords: p-Laplace, eigenfunction, Finsler metric, Cheeger set, anisotropic isoperimetric inequality.

MSC: 35J20, 35J70, 49A52, 49G05, 52A05, 52A40

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