Journal Home Page Cumulative Index List of all Volumes Complete Contentsof this Volume Previous Article Journal of Convex Analysis 15 (2008), No. 3, 623--634Copyright 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 kawohl@math.uni-koeln.de Matteo Novaga Dip. di Matematica, Università di Pisa, Largo B. Pontecorvo 5, 56127 Pisa, Italy novaga@dm.unipi.it [Abstract-pdf] 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 [ Fulltext-pdf  (149  KB)] for subscribers only.