Gradient regularity for a class of elliptic obstacle problems

2024/08/18 by Giova, Raffaella, Grimaldi, Antonio Giuseppe, Torricelli, Andrea · 2 citations
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2408.09510

Abstract

We prove some regularity results for a priori bounded local minimizers of non-autonomous integral functionals of the form F(v,Ω)=∫_ΩF(x,Dv)dx, under the constraint v ≥ ψ a.e. in Ω, where ψ is a fixed obstacle function. Assuming that the coefficients of the partial map x ↦ D_ξF(x,ξ) satisfy a suitable Sobolev regularity, we are able to obtain higher differentiability and Lipschitz continuity results for the local minimizers.

Cited by

• Regularity for minimizers of degenerate, non-autonomous, orthotropic integral functionals
• Local Lipschitz continuity for energy integrals with fast growth and lower order terms

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• Regularity for Obstacle Problems without Structure Conditions
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• Higher differentiability results for solutions to a class of non-autonomous obstacle problems with sub-quadratic growth conditions