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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2409.08796 |
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| _version_ | 1866909314727280640 |
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| author | Grimaldi, Antonio Giuseppe Russo, Stefania |
| author_facet | Grimaldi, Antonio Giuseppe Russo, Stefania |
| contents | We establish the higher fractional differentiability for the minimizers of non-autonomous integral functionals of the form \begin{equation}
\mathcal{F}(u,Ω):=\int_Ω\left[ f(x,Du)- g \cdot u \right] dx , \notag \end{equation} under $(p,q)$-growth conditions. Besides a suitable differentiability assumption on the partial map $x \mapsto D_ξf(x,ξ)$, we do not need to assume any differentiability assumption on the function $g$. Moreover, we show that the higher differentiability result holds true also assuming strict convexity and growth conditions on $f$ only at infinity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_08796 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Regularity results for minimizers of non-autonomous integral functionals Grimaldi, Antonio Giuseppe Russo, Stefania Analysis of PDEs We establish the higher fractional differentiability for the minimizers of non-autonomous integral functionals of the form \begin{equation} \mathcal{F}(u,Ω):=\int_Ω\left[ f(x,Du)- g \cdot u \right] dx , \notag \end{equation} under $(p,q)$-growth conditions. Besides a suitable differentiability assumption on the partial map $x \mapsto D_ξf(x,ξ)$, we do not need to assume any differentiability assumption on the function $g$. Moreover, we show that the higher differentiability result holds true also assuming strict convexity and growth conditions on $f$ only at infinity. |
| title | Regularity results for minimizers of non-autonomous integral functionals |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2409.08796 |