Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2412.21048 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917881387679744 |
|---|---|
| author | Cejas, María Eugenia Durán, Ricardo G. |
| author_facet | Cejas, María Eugenia Durán, Ricardo G. |
| contents | Given a bounded domain $Ø$ and $f$ of zero integral, the existence of a vector fields $\u$ vanishing on $\partialØ$ and satisfying $\d\u=f$ has been widely studied because of its connection with many important problems. It is known that for $f\in L^p(Ø)$, $1<p<\infty$, there exists a solution $\u\in W^{1,p}_0(Ø)$, and also that an analogous result is not true for $p=1$ or $p=\infty$. The goal of this paper is to prove results for Hardy spaces when $\frac{n}{n+1}<p\le 1$, and in the other limiting case, for bounded mean oscillation and Lipschitz spaces. As a byproduct of our analysis we obtain a Korn inequality for vector fields in Hardy-Sobolev spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_21048 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Solutions of the divergence equation in Hardy and lipschitz spaces Cejas, María Eugenia Durán, Ricardo G. Analysis of PDEs Functional Analysis Given a bounded domain $Ø$ and $f$ of zero integral, the existence of a vector fields $\u$ vanishing on $\partialØ$ and satisfying $\d\u=f$ has been widely studied because of its connection with many important problems. It is known that for $f\in L^p(Ø)$, $1<p<\infty$, there exists a solution $\u\in W^{1,p}_0(Ø)$, and also that an analogous result is not true for $p=1$ or $p=\infty$. The goal of this paper is to prove results for Hardy spaces when $\frac{n}{n+1}<p\le 1$, and in the other limiting case, for bounded mean oscillation and Lipschitz spaces. As a byproduct of our analysis we obtain a Korn inequality for vector fields in Hardy-Sobolev spaces. |
| title | Solutions of the divergence equation in Hardy and lipschitz spaces |
| topic | Analysis of PDEs Functional Analysis |
| url | https://arxiv.org/abs/2412.21048 |