Calculus of Variations and Geometric Measure Theory
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M. Eleuteri - J. Habermann

Regularity results for a class of obstacle problems under non standard growth conditions

created by eleuteri on 15 Oct 2009
modified on 02 Dec 2013


Published Paper

Inserted: 15 oct 2009
Last Updated: 2 dec 2013

Journal: J. Math. Anal. Appl.
Volume: 344
Number: 2
Year: 2008


We prove regularity results for minimizers of functionals $\cF(u,\Omega) := \int_\Omega f(x,u,Du)\, dx$ in the class $K := \{ u \in W^{1,p(x)}(\Omega,\R): u \ge \psi\}$, where $\psi:\Omega \to \R$ is a fixed function and $f$ is quasiconvex and fulfills a growth condition of the type $$ L{-1}
{p(x)} \le f(x,\xi,z) \le L(1+
{p(x)}), $$ with growth exponent $p:\Omega \to (1,\infty)$.

Keywords: Non standard growth conditions, obstacle problems


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