Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2505.01611 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913816987566080 |
|---|---|
| author | Plakhov, Alexander Protasov, Vladimir |
| author_facet | Plakhov, Alexander Protasov, Vladimir |
| contents | We consider inequalities between $L_p$-norms of partial derivatives, $p\in [1,+\infty]$, for bivariate concave functions on a convex domain that vanish on the boundary. Can the ratio between those norms be arbitrarily large? If not, what is the upper bound? We show that for $p=1$, the ratio is always bounded and find sharp estimates, while for $p>1$, the answer depends on the geometry of the domain. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_01611 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On inequalities between norms of partial derivatives on convex domains Plakhov, Alexander Protasov, Vladimir Classical Analysis and ODEs Functional Analysis Optimization and Control 26D10, 49K21, 52A10 We consider inequalities between $L_p$-norms of partial derivatives, $p\in [1,+\infty]$, for bivariate concave functions on a convex domain that vanish on the boundary. Can the ratio between those norms be arbitrarily large? If not, what is the upper bound? We show that for $p=1$, the ratio is always bounded and find sharp estimates, while for $p>1$, the answer depends on the geometry of the domain. |
| title | On inequalities between norms of partial derivatives on convex domains |
| topic | Classical Analysis and ODEs Functional Analysis Optimization and Control 26D10, 49K21, 52A10 |
| url | https://arxiv.org/abs/2505.01611 |