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

Bernd Kawohl; Matteo Novaga

Abstract

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

.

Author information

Contact details are reproduced from the original publication and may be historical.

Bernd Kawohl

Mathematisches Institut, Universitaet Koeln, 50923 Koeln, Germany

kawohl@math.uni-koeln.de

Matteo Novaga

Dip. di Matematica, Università di Pisa, Largo B. Pontecorvo 5, 56127 Pisa, Italy

novaga@dm.unipi.it

Keywords

p-Laplace
eigenfunction
Finsler metric
Cheeger set
anisotropic isoperimetric inequality

Mathematics Subject Classification

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

Suggested citation

B. Kawohl, M. Novaga. “The p-Laplace Eigenvalue Problem as p Approaches 1 and Cheeger Sets in a Finsler Metric.” Journal of Convex Analysis 15 (2008), No. 3, 623–634.