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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/2507.18474 |
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| _version_ | 1866912499872301056 |
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| author | Almi, Stefano Leone, Chiara Manzo, Gianluigi |
| author_facet | Almi, Stefano Leone, Chiara Manzo, Gianluigi |
| contents | We prove higher integrability for local minimizers of the double-phase orthotropic functional \[
\sum_{i=1}^{n}\int_Ω\left(\left|u_{x_i}\right|^p+a(x)\left| u_{x_i}\right|^q\right)dx \] when the weight function $a \geq0$ is assumed to be $α$-Hölder continuous, while the exponents $p, q$ are such that $2 \leq p \leq q$ and $\frac{q}{p} < 1 + \fracα{n}$. Under natural Sobolev regularity of~$a$, we further obtain explicit Lipschitz regularity estimates for local minimizers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_18474 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Gradient regularity for double-phase orthotropic functionals Almi, Stefano Leone, Chiara Manzo, Gianluigi Analysis of PDEs 35J70, 35B65 We prove higher integrability for local minimizers of the double-phase orthotropic functional \[ \sum_{i=1}^{n}\int_Ω\left(\left|u_{x_i}\right|^p+a(x)\left| u_{x_i}\right|^q\right)dx \] when the weight function $a \geq0$ is assumed to be $α$-Hölder continuous, while the exponents $p, q$ are such that $2 \leq p \leq q$ and $\frac{q}{p} < 1 + \fracα{n}$. Under natural Sobolev regularity of~$a$, we further obtain explicit Lipschitz regularity estimates for local minimizers. |
| title | Gradient regularity for double-phase orthotropic functionals |
| topic | Analysis of PDEs 35J70, 35B65 |
| url | https://arxiv.org/abs/2507.18474 |