Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2501.11766 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909784885690368 |
|---|---|
| author | Korobenko, Lyudmila |
| author_facet | Korobenko, Lyudmila |
| contents | We develop regularity theory for degenerate elliptic equations with the degeneracy controlled by a weight. More precisely, we show local boundedness and continuity of weak solutions under the assumption of a weighted Orlicz-Sobolev and Poincaré inequalities. The proof relies on a modified DeGiorgi iteration scheme, developed in arXiv:1608.01630 and arXiv:1703.00774. The Orlicz-Sobolev inequality we assume here is much weaker than the classical $(2σ,2)$ Sobolev inequality with $σ>1$ which is typically used in the DeGiorgi or Moser iteration. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_11766 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Degenerate elliptic equations with $Φ$-admissible weights Korobenko, Lyudmila Analysis of PDEs We develop regularity theory for degenerate elliptic equations with the degeneracy controlled by a weight. More precisely, we show local boundedness and continuity of weak solutions under the assumption of a weighted Orlicz-Sobolev and Poincaré inequalities. The proof relies on a modified DeGiorgi iteration scheme, developed in arXiv:1608.01630 and arXiv:1703.00774. The Orlicz-Sobolev inequality we assume here is much weaker than the classical $(2σ,2)$ Sobolev inequality with $σ>1$ which is typically used in the DeGiorgi or Moser iteration. |
| title | Degenerate elliptic equations with $Φ$-admissible weights |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2501.11766 |