On the Hölder continuity of signed solutions to doubly nonlinear parabolic equations in the mixed degenerate/singular cases
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2026
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866910023847772160 |
|---|---|
| author | Skrypnik, Igor I. |
| author_facet | Skrypnik, Igor I. |
| contents | We prove the Hölder continuity of sign-changing solutions to the equation of the type $$\frac{\partial}{\partial t}\big(|u|^{q-1} u\big)- div\Big(|D u|^{p-2}\,D u\Big)=0,$$ where numbers $p$, $q$ satisfy the conditions $$0<q<p-1\quad \text{and}\quad p<2,$$ or $$q>p-1\quad\text{and}\quad p>2.$$ Our proof uses new versions of the integral Harnack type inequalities for sign-changing solutions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_14800 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the Hölder continuity of signed solutions to doubly nonlinear parabolic equations in the mixed degenerate/singular cases Skrypnik, Igor I. Analysis of PDEs 35B40, 35B45, 35B65, 35K65, 35K67 We prove the Hölder continuity of sign-changing solutions to the equation of the type $$\frac{\partial}{\partial t}\big(|u|^{q-1} u\big)- div\Big(|D u|^{p-2}\,D u\Big)=0,$$ where numbers $p$, $q$ satisfy the conditions $$0<q<p-1\quad \text{and}\quad p<2,$$ or $$q>p-1\quad\text{and}\quad p>2.$$ Our proof uses new versions of the integral Harnack type inequalities for sign-changing solutions. |
| title | On the Hölder continuity of signed solutions to doubly nonlinear parabolic equations in the mixed degenerate/singular cases |
| topic | Analysis of PDEs 35B40, 35B45, 35B65, 35K65, 35K67 |
| url | https://arxiv.org/abs/2602.14800 |