Boundary regularity of a fourth order Alt-Caffarelli problem and applications to the minimization of the critical buckling load
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912780273057792 |
|---|---|
| author | Lamboley, Jimmy Nahon, Mickaël |
| author_facet | Lamboley, Jimmy Nahon, Mickaël |
| contents | We study a higher order analogue to the Alt-Caffarelli functional that arises in several shape optimization problems, among which the minimization of the critical buckling load of a clamped plate of fixed area. We obtain several regularity results up to the boundary in two dimensions, in particular we prove the full regularity of the boundary (analytic outside angles of opening $\approx 1.43π$) near any point of density less than 1 of the optimal shape. These results are based on the monotonicity formula discovered by Dipierro, Karakhanyan, and Valdinoci, which we improve with a new epiperimetric inequality. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_18626 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Boundary regularity of a fourth order Alt-Caffarelli problem and applications to the minimization of the critical buckling load Lamboley, Jimmy Nahon, Mickaël Analysis of PDEs Optimization and Control 35R35, 31A30, 49Q10, 35B65, 35N25, 35A16 We study a higher order analogue to the Alt-Caffarelli functional that arises in several shape optimization problems, among which the minimization of the critical buckling load of a clamped plate of fixed area. We obtain several regularity results up to the boundary in two dimensions, in particular we prove the full regularity of the boundary (analytic outside angles of opening $\approx 1.43π$) near any point of density less than 1 of the optimal shape. These results are based on the monotonicity formula discovered by Dipierro, Karakhanyan, and Valdinoci, which we improve with a new epiperimetric inequality. |
| title | Boundary regularity of a fourth order Alt-Caffarelli problem and applications to the minimization of the critical buckling load |
| topic | Analysis of PDEs Optimization and Control 35R35, 31A30, 49Q10, 35B65, 35N25, 35A16 |
| url | https://arxiv.org/abs/2512.18626 |