Least gradient problem with Dirichlet condition imposed on a part of the boundary

2020/09/09 by Wojciech Górny, Górny, Wojciech
Computer Science · Mathematics · #35J20 #35J25 #35J75 #35J92 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Contact Mechanics and Variational Inequalities #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2009.04048

openalex publication_date 2020/09/09 · openalex created_date 2024/02/13 · openalex updated_date 2026/07/28

Abstract

We provide an analysis of the least gradient problem in the case when the boundary datum is only imposed on a part of the boundary. First, we give a characterisation of solutions in a general setting using convex duality theory. Then, we discuss the way in which solutions attain their boundary values, structure of solutions and their regularity.

Related

• Special cases of the planar least gradient problem
• Existence of minimisers in the least gradient problem for general boundary data
• The non-convex planar Least Gradient Problem
• The planar Least Gradient problem in convex domains
• The planar Least Gradient problem in convex domains, the case of continuous datum