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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2402.06252 |
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| _version_ | 1866912154156793856 |
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| author | Schäffner, Mathias |
| author_facet | Schäffner, Mathias |
| contents | We study local regularity properties of local minimizer of scalar integral functionals with controlled $(p,q)$-growth in the two-dimensional plane. We establish Lipschitz continuity for local minimizer under the condition $1<p\leq q<\infty$ with $q<3p$ which improve upon the classical results valid in the regime $q<2p$. Along the way, we establish an $L^\infty$-$L^2$-estimate for solutions of linear uniformly elliptic equations in the plane which is optimal with respect to the ellipticity contrast of the coefficients. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_06252 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Lipschitz bounds for nonuniformly elliptic integral functionals in the plane Schäffner, Mathias Analysis of PDEs We study local regularity properties of local minimizer of scalar integral functionals with controlled $(p,q)$-growth in the two-dimensional plane. We establish Lipschitz continuity for local minimizer under the condition $1<p\leq q<\infty$ with $q<3p$ which improve upon the classical results valid in the regime $q<2p$. Along the way, we establish an $L^\infty$-$L^2$-estimate for solutions of linear uniformly elliptic equations in the plane which is optimal with respect to the ellipticity contrast of the coefficients. |
| title | Lipschitz bounds for nonuniformly elliptic integral functionals in the plane |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2402.06252 |