Gradient higher integrability of bounded solutions to parabolic double-phase systems
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912759781785600 |
|---|---|
| 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 |