期刊
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
卷 223, 期 -, 页码 -出版社
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.na.2022.113012
关键词
Least gradient problem; Optimal transport; Dirichlet region
In this paper, we study the BV least gradient problem with Dirichlet condition imposed on a part of the boundary. We establish the equivalence between this problem and an optimal transport problem. By analyzing the summability of the transport density, we prove the existence, uniqueness, and regularity of the solution to the least gradient problem.
In this paper, we consider the BV least gradient problem with Dirichlet condition imposed on a part Gamma of the boundary partial derivative Omega. In 2D, we show that this problem is equivalent to an optimal transport problem with Dirichlet region partial derivative Omega\Gamma. Thanks to this equivalence, we show existence and uniqueness of a solution u to this least gradient problem. Then, we prove W-1,W-p regularity on this solution u by studying the L-p summability of the transport density in the corresponding equivalent optimal transport formulation. (c) 2022 Published by Elsevier Ltd.
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