Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2502.11980 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909500588425216 |
|---|---|
| author | Raiţă, Bogdan |
| author_facet | Raiţă, Bogdan |
| contents | We show that Müller's $L\log L$ bound $$F(Du)\geq 0,\,Du\in L^p_{\mathrm{loc}}(\mathbb{R}^n)\implies F(Du)\in L\log L_{\mathrm{loc}}(\mathbb{R}^n)$$ for $F =\det$ and $p=n$ holds for quasiconcave $F$ which are homogeneous of degree $p>1$. This contrasts similar Hardy space bounds which hold only for null Lagrangians. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_11980 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quasiconvexity and self-improving size estimates Raiţă, Bogdan Analysis of PDEs Primary: 49J45, Secondary: 28B05 We show that Müller's $L\log L$ bound $$F(Du)\geq 0,\,Du\in L^p_{\mathrm{loc}}(\mathbb{R}^n)\implies F(Du)\in L\log L_{\mathrm{loc}}(\mathbb{R}^n)$$ for $F =\det$ and $p=n$ holds for quasiconcave $F$ which are homogeneous of degree $p>1$. This contrasts similar Hardy space bounds which hold only for null Lagrangians. |
| title | Quasiconvexity and self-improving size estimates |
| topic | Analysis of PDEs Primary: 49J45, Secondary: 28B05 |
| url | https://arxiv.org/abs/2502.11980 |