Improved regularity estimates for Hardy-Hénon-type equations driven by the $\infty$-Laplacian
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909366272131072 |
|---|---|
| author | Júnior, Elzon C. Bezerra da Silva, João Vitor Nascimento, Thialita M. Sá, Ginaldo S. |
| author_facet | Júnior, Elzon C. Bezerra da Silva, João Vitor Nascimento, Thialita M. Sá, Ginaldo S. |
| contents | In this work, we establish sharp and improved regularity estimates for viscosity solutions of Hardy-Hénon-type equations with possibly singular weights and strong absorption governed by the $\infty$-Laplacian $$
Δ_{\infty} u(x) = |x|^αu_+^m(x) \quad \text{in} \quad B_1, $$ under suitable assumptions on the data. In this setting, we derive an explicit regularity exponent that depends only on universal parameters. Additionally, we prove non-degeneracy properties, providing further geometric insights into the nature of these solutions. Our regularity estimates not only improve but also extend, to some extent, the previously obtained results for zero-obstacle and dead-core problems driven by the $\infty$-Laplacian. As an application of our findings, we also address some Liouville-type results for this class of equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_19970 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Improved regularity estimates for Hardy-Hénon-type equations driven by the $\infty$-Laplacian Júnior, Elzon C. Bezerra da Silva, João Vitor Nascimento, Thialita M. Sá, Ginaldo S. Analysis of PDEs 35B65, 35J60, 35J94 In this work, we establish sharp and improved regularity estimates for viscosity solutions of Hardy-Hénon-type equations with possibly singular weights and strong absorption governed by the $\infty$-Laplacian $$ Δ_{\infty} u(x) = |x|^αu_+^m(x) \quad \text{in} \quad B_1, $$ under suitable assumptions on the data. In this setting, we derive an explicit regularity exponent that depends only on universal parameters. Additionally, we prove non-degeneracy properties, providing further geometric insights into the nature of these solutions. Our regularity estimates not only improve but also extend, to some extent, the previously obtained results for zero-obstacle and dead-core problems driven by the $\infty$-Laplacian. As an application of our findings, we also address some Liouville-type results for this class of equations. |
| title | Improved regularity estimates for Hardy-Hénon-type equations driven by the $\infty$-Laplacian |
| topic | Analysis of PDEs 35B65, 35J60, 35J94 |
| url | https://arxiv.org/abs/2410.19970 |