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The non-convex planar Least Gradient Problem
- Publication Year :
- 2024
-
Abstract
- 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.
- Subjects :
- Mathematics - Analysis of PDEs
26A45, 35J20, 35J25, 35A15, 49Q22
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2408.13064
- Document Type :
- Working Paper