Gradient higher integrability of bounded solutions to parabolic double-phase systems

Fuente: arXiv
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Main Authors: Chlebicka, Iwona, Garain, Prashanta, Kim, Wontae
Format: Preprint
Published: 2025
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author Chlebicka, Iwona
Garain, Prashanta
Kim, Wontae
author_facet Chlebicka, Iwona
Garain, Prashanta
Kim, Wontae
contents We prove that bounded solutions to degenerate parabolic double-phase problem modelled upon \[u_t-\dv(|\na u|^{p-2}\na u+a(x,t)|\na u|^{q-2}\na u)=-\dv(|F|^{p-2}F+a(x,t)|F|^{q-2}F)\,, \] where a nonnegative weight $a$ is $α$-Hölder continuous in space and $\tfrac α2$-Hölder continuous in time, have locally higher integrable gradients for the sharp range of exponents $p<q\le p+α$.
format Preprint
id arxiv_https___arxiv_org_abs_2512_11294
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Gradient higher integrability of bounded solutions to parabolic double-phase systems
Chlebicka, Iwona
Garain, Prashanta
Kim, Wontae
Analysis of PDEs
35D30, 35K55, 35K65
We prove that bounded solutions to degenerate parabolic double-phase problem modelled upon \[u_t-\dv(|\na u|^{p-2}\na u+a(x,t)|\na u|^{q-2}\na u)=-\dv(|F|^{p-2}F+a(x,t)|F|^{q-2}F)\,, \] where a nonnegative weight $a$ is $α$-Hölder continuous in space and $\tfrac α2$-Hölder continuous in time, have locally higher integrable gradients for the sharp range of exponents $p<q\le p+α$.
title Gradient higher integrability of bounded solutions to parabolic double-phase systems
topic Analysis of PDEs
35D30, 35K55, 35K65
url https://arxiv.org/abs/2512.11294