Least gradient problem on annuli

2019/08/24 by Samer Dweik, Dweik, Samer, Wojciech Górny +1
Mathematics · #35J20 #35J25 #35J75 #35J92 #Analysis of PDEs (math.AP) #FOS: Mathematics #Optimization and Control (math.OC) #math.AP #math.OC #msc:35J20 #msc:35J25 #msc:35J75 #msc:35J92

paper · pdf · doi:10.48550/arxiv.1908.09113

19 pages, 1 figure

arxiv created 2019/08/24 · arxiv updated 2019/08/27

Abstract

We consider the two dimensional BV least gradient problem on an annulus with given boundary data g ∈ BV(∂Ω). Firstly, we prove that this problem is equivalent to the optimal transport problem with source and target measures located on the boundary of the domain. Then, under some admissibility conditions on the trace, we show that there exists a unique solution for the BV least gradient problem. Moreover, we prove some L^p estimates on the corresponding minimal flow of the Beckmann problem, which implies directly W^1,p regularity for the solution of the BV least gradient problem.

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