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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2512.04281 |
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| _version_ | 1866915653197234176 |
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| author | Grimaldi, Antonio Giuseppe Russo, Stefania |
| author_facet | Grimaldi, Antonio Giuseppe Russo, Stefania |
| contents | We prove the higher differentiability of integer order of locally bounded minimizers of integral functionals of the form \begin{equation*}
\mathcal{F}(u,Ω):= \,\sum_{i=1}^{n} \dfrac{1}{p_i}\displaystyle \int_Ω\, a_i(x) \lvert u_{x_i} \rvert^{p_i} dx- \int_Ωω(x)u(x) dx, \end{equation*} where the exponents $ p_i \geq 2 $ and the coefficients $ a_i(x) $ satisfy a suitable Sobolev regularity. The main novelty consists in dealing with non-autonomous, anisotropic functionals, which depend also on the solution. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_04281 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Regularity for minimizers of degenerate, non-autonomous, orthotropic integral functionals Grimaldi, Antonio Giuseppe Russo, Stefania Analysis of PDEs We prove the higher differentiability of integer order of locally bounded minimizers of integral functionals of the form \begin{equation*} \mathcal{F}(u,Ω):= \,\sum_{i=1}^{n} \dfrac{1}{p_i}\displaystyle \int_Ω\, a_i(x) \lvert u_{x_i} \rvert^{p_i} dx- \int_Ωω(x)u(x) dx, \end{equation*} where the exponents $ p_i \geq 2 $ and the coefficients $ a_i(x) $ satisfy a suitable Sobolev regularity. The main novelty consists in dealing with non-autonomous, anisotropic functionals, which depend also on the solution. |
| title | Regularity for minimizers of degenerate, non-autonomous, orthotropic integral functionals |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2512.04281 |