Calculus of Variations and Geometric Measure Theory

G. Buttazzo - B. Kawohl

Overdetermined boundary value problems for the $\infty$-Laplacian

created by buttazzo on 13 Nov 2009
modified on 04 Mar 2010



Inserted: 13 nov 2009
Last Updated: 4 mar 2010

Year: 2009


We consider overdetermined boundary value problems for the $\infty$-Laplacian in a domain $\Omega$ of $*R*^n$ and discuss what kind of implications on the geometry of $\Omega$ the existence of a solution may have. The classical $\infty$-Laplacian, the normalized or game-theoretic $\infty$-Laplacian and the limit of the $p$-Laplacian as $p\to\infty$ are considered and provide different answers.

Keywords: viscosity solution, overdetermined bvp, degenerate elliptic equation, web-function, cut locus, ridge set