Least gradient problem with respect to a non-strictly convex norm

2018/06/05 by Górny, Wojciech
#35J20 #35J25 #35J75 #35J92 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1806.01921

Abstract

We study the planar least gradient problem with respect to an anisotropic norm ϕ for continuous boundary data. We prove existence of minimizers for strictly convex domains Ω. Furthermore, we inspect the issue of uniqueness and regularity of minimizers only in terms of the modes of convexity of ϕ and Ω. The results are independent from the regularity of ϕ.

Related

• Planar least gradient problem: existence, regularity and anisotropic\n case
• Special cases of the planar least gradient problem
• The planar Least Gradient problem in convex domains
• Existence of minimisers in the least gradient problem for general boundary data
• The planar Least Gradient problem in convex domains, the case of continuous datum