The non-convex planar Least Gradient Problem
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910575040135168 |
|---|---|
| author | Dweik, Samer Rybka, Piotr Sabra, Ahmad |
| author_facet | Dweik, Samer Rybka, Piotr Sabra, Ahmad |
| contents | We study the least gradient problem in bounded regions with Lipschitz boundary in the plane. We provide a set of conditions for the existence of solutions in non-convex simply connected regions. We assume the boundary data is continuous and in the space of functions of bounded variation, and we are interested in solutions that satisfy the boundary conditions in the trace sense. Our method relies on the equivalence of the least gradient problem and the Beckman problem which allows us to use the tools of the optimal transportation theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_13064 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The non-convex planar Least Gradient Problem Dweik, Samer Rybka, Piotr Sabra, Ahmad Analysis of PDEs 26A45, 35J20, 35J25, 35A15, 49Q22 We study the least gradient problem in bounded regions with Lipschitz boundary in the plane. We provide a set of conditions for the existence of solutions in non-convex simply connected regions. We assume the boundary data is continuous and in the space of functions of bounded variation, and we are interested in solutions that satisfy the boundary conditions in the trace sense. Our method relies on the equivalence of the least gradient problem and the Beckman problem which allows us to use the tools of the optimal transportation theory. |
| title | The non-convex planar Least Gradient Problem |
| topic | Analysis of PDEs 26A45, 35J20, 35J25, 35A15, 49Q22 |
| url | https://arxiv.org/abs/2408.13064 |