Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2405.00231 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866916230425739264 |
|---|---|
| author | Lewicka, Marta |
| author_facet | Lewicka, Marta |
| contents | We prove a convex integration result for the Monge-Ampère system, in case of dimension $d=2$ and arbitrary codimension $k\geq 1$. Our prior result stated flexibility up to the Hölder regularity $\mathcal{C}^{1,\frac{1}{1+ 4/k}}$, whereas presently we achieve flexibility up to $\mathcal{C}^{1,1}$ when $k\geq 4$ and up to $\mathcal{C}^{1,\frac{2^k-1}{2^{k+1}-1}}$ for any $k$. This first result uses the approach of Källen, while the second result iterates on the approach of Cao-Hirsch-Inauen and agrees with it for $k=1$ at the Hölder regularity up to $\mathcal{C}^{1,1/3}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_00231 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Monge-Ampere system in dimension two: a further regularity improvement Lewicka, Marta Analysis of PDEs We prove a convex integration result for the Monge-Ampère system, in case of dimension $d=2$ and arbitrary codimension $k\geq 1$. Our prior result stated flexibility up to the Hölder regularity $\mathcal{C}^{1,\frac{1}{1+ 4/k}}$, whereas presently we achieve flexibility up to $\mathcal{C}^{1,1}$ when $k\geq 4$ and up to $\mathcal{C}^{1,\frac{2^k-1}{2^{k+1}-1}}$ for any $k$. This first result uses the approach of Källen, while the second result iterates on the approach of Cao-Hirsch-Inauen and agrees with it for $k=1$ at the Hölder regularity up to $\mathcal{C}^{1,1/3}$. |
| title | The Monge-Ampere system in dimension two: a further regularity improvement |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2405.00231 |