We prove some regularity results for a priori bounded local minimizers of non-autonomous integral functionals of the form (Formula presented.) 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↦DξF(x,ξ) satisfy a suitable Sobolev regularity, we are able to obtain higher differentiability and Lipschitz continuity results for the local minimizers.
Gradient regularity for a class of elliptic obstacle problems
Giova, Raffaella
;Grimaldi, Antonio Giuseppe;
2025-01-01
Abstract
We prove some regularity results for a priori bounded local minimizers of non-autonomous integral functionals of the form (Formula presented.) 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↦DξF(x,ξ) satisfy a suitable Sobolev regularity, we are able to obtain higher differentiability and Lipschitz continuity results for the local minimizers.File in questo prodotto:
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