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Autores principales: Dweik, Samer, Rybka, Piotr, Sabra, Ahmad
Formato: Preprint
Publicado: 2024
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Acceso en línea:https://arxiv.org/abs/2408.13064
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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