Gradient regularity for a class of elliptic obstacle problems
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866916361326821376 |
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| author | Giova, Raffaella Grimaldi, Antonio Giuseppe Torricelli, Andrea |
| author_facet | Giova, Raffaella Grimaldi, Antonio Giuseppe Torricelli, Andrea |
| contents | We prove some regularity results for a priori bounded local minimizers of non-autonomous integral functionals of the form $$\mathcal{F}(v,Ω)=\int_ΩF(x,Dv)dx,$$ under the constraint $v \ge ψ$ a.e. in $Ω$, where $ψ$ is a fixed obstacle function. Assuming that the coefficients of the partial map $x \mapsto D_ξF(x,ξ)$ satisfy a suitable Sobolev regularity, we are able to obtain higher differentiability and Lipschitz continuity results for the local minimizers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_09510 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Gradient regularity for a class of elliptic obstacle problems Giova, Raffaella Grimaldi, Antonio Giuseppe Torricelli, Andrea Analysis of PDEs We prove some regularity results for a priori bounded local minimizers of non-autonomous integral functionals of the form $$\mathcal{F}(v,Ω)=\int_ΩF(x,Dv)dx,$$ under the constraint $v \ge ψ$ a.e. in $Ω$, where $ψ$ is a fixed obstacle function. Assuming that the coefficients of the partial map $x \mapsto D_ξF(x,ξ)$ satisfy a suitable Sobolev regularity, we are able to obtain higher differentiability and Lipschitz continuity results for the local minimizers. |
| title | Gradient regularity for a class of elliptic obstacle problems |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2408.09510 |