Regularity results for a class of obstacle problems with $p,q-$growth conditions

Abstract

In this paper we prove the local boundedness as well as the local Lipschitz continuity for solutions to a class of obstacle problems of the type $$\min \left\{{\int }_{\Omega }F(x,Dz):z\in {\mathcal{K}}_{\psi }(\Omega )\right\}.$$ Here ${\mathcal{K}}_{\psi }(\Omega )$ is set of admissible functions $z\in W^{1,p}(\Omega )$ such that $z\ge \psi$ a.e. in $\Omega$, $\psi$ being the obstacle and $\Omega$ being an open bounded set of ${\mathbb{R}}^n$, $n\ge 2$. The main novelty here is that we are assuming $F(x,Dz)$ satisfying $(p,q)$-growth conditions {and less restrictive assumptions on the obstacle with respect to the existing regularity results}.

References in corpus (4)

• Regularity for minimizers for functionals of double phase with variable exponents
• Double phase image restoration
• Regularity results for solutions to obstacle problems with Sobolev coeffcients
• Lipschitz continuity results for a class of obstacle problems