M. Eleuteri, WIAS - Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstrasse 39, 10117 Berlin, Germany, e-mail: eleuteri@wias-berlin.de; on leave from: Dipartimento di Matematica, Universita di Trento, via Sommarive 14, 38050 Povo (Trento), Italy, e-mail: eleuteri@science.unitn.it
Abstract: We prove some optimal regularity results for minimizers of the integral functional $\int f(x,u,Du)\dd x$ belonging to the class $ K:=\{u \in W^{1,p}(\Omega) u\ge\psi\}$, where $\psi$ is a fixed function, under standard growth conditions of $p$-type, i.e.
L^{-1}|z|^p \le f(x,s,z) \le L(1+|z|^p).
Keywords: regularity results, local minimizers, integral functionals, obstacle problems, standard growth conditions
Classification (MSC 2000): 49N60, 35J85, 49J40
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