Higher Differentiability of Minimizers for Non-Autonomous Orthotropic Functionals
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866913714558468096 |
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| author | Russo, Stefania |
| author_facet | Russo, Stefania |
| contents | We establish the higher differentiability for the minimizers of the following non-autonomous integral functionals \begin{equation*}
\mathcal{F}(u,Ω):= \, \int_Ω\sum_{i=1}^{n} \, a_i(x) \lvert u_{x_i} \rvert^{p_i} dx, \end{equation*} with exponents $p_i \geq 2$ and with coefficients $a_i(x)$ that satisfy a suitable Sobolev regularity. The main result is obtained, as usual, by imposing a gap bound on the exponents $p_i$, which depends on the dimension and on the degree of regularity of the coefficients $a_i(x)$ |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_00869 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Higher Differentiability of Minimizers for Non-Autonomous Orthotropic Functionals Russo, Stefania Analysis of PDEs 35J70, 35B65, 49K20 We establish the higher differentiability for the minimizers of the following non-autonomous integral functionals \begin{equation*} \mathcal{F}(u,Ω):= \, \int_Ω\sum_{i=1}^{n} \, a_i(x) \lvert u_{x_i} \rvert^{p_i} dx, \end{equation*} with exponents $p_i \geq 2$ and with coefficients $a_i(x)$ that satisfy a suitable Sobolev regularity. The main result is obtained, as usual, by imposing a gap bound on the exponents $p_i$, which depends on the dimension and on the degree of regularity of the coefficients $a_i(x)$ |
| title | Higher Differentiability of Minimizers for Non-Autonomous Orthotropic Functionals |
| topic | Analysis of PDEs 35J70, 35B65, 49K20 |
| url | https://arxiv.org/abs/2503.00869 |