Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2022
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2212.14757 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909414313689088 |
|---|---|
| author | Carbotti, Alessandro Cito, Simone La Manna, Domenico Angelo Pallara, Diego |
| author_facet | Carbotti, Alessandro Cito, Simone La Manna, Domenico Angelo Pallara, Diego |
| contents | The aim of this paper is to give a new proof that any very weak $s$-harmonic function $u$ in the unit ball $B$ is smooth. As a first step, we improve the local summability properties of $u$. Then, we exploit a suitable version of the difference quotient method tailored to get rid of the singularity of the integral kernel and gain Sobolev regularity and local linear estimates of the $H^{s}_{\rm loc}$ norm of $u$. Finally, by applying more standard methods, such as elliptic regularity and Schauder estimates, we reach real analyticity of $u$. Up to the authors' knowledge, the difference quotient techniques are new. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_14757 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Local Regularity of very weak $s$-harmonic functions via fractional difference quotients Carbotti, Alessandro Cito, Simone La Manna, Domenico Angelo Pallara, Diego Analysis of PDEs The aim of this paper is to give a new proof that any very weak $s$-harmonic function $u$ in the unit ball $B$ is smooth. As a first step, we improve the local summability properties of $u$. Then, we exploit a suitable version of the difference quotient method tailored to get rid of the singularity of the integral kernel and gain Sobolev regularity and local linear estimates of the $H^{s}_{\rm loc}$ norm of $u$. Finally, by applying more standard methods, such as elliptic regularity and Schauder estimates, we reach real analyticity of $u$. Up to the authors' knowledge, the difference quotient techniques are new. |
| title | Local Regularity of very weak $s$-harmonic functions via fractional difference quotients |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2212.14757 |