Calculus of Variations and Geometric Measure Theory

M. Chermisi - E. Valdinoci

Fibered nonlinearities for $p(x)$-Laplace equations

created by chermisi on 17 Sep 2008
modified on 15 Apr 2010


Published Paper

Inserted: 17 sep 2008
Last Updated: 15 apr 2010

Journal: Advances in Calculus of Variations
Year: 2009


In $\R^m\times\R^{n-m}$, endowed with coordinates $X=(x,y)$, we consider the PDE $$ -{\rm div}\, \big( \alpha(\x)
\nabla u(\X)
{p(x)-2}\nabla u(\X)\big)=f(x,u(\X)).$$ We prove a geometric inequality and a symmetry result.