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Main Authors: Almi, Stefano, Leone, Chiara, Manzo, Gianluigi
Format: Preprint
Published: 2025
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Online Access:https://arxiv.org/abs/2507.18474
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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