Special cases of the planar least gradient problem

2016/04/29 by Górny, Wojciech, Rybka, Piotr, Sabra, Ahmad
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1605.00035

Abstract

We study two special cases of the planar least gradient problem. In the first one, the boundary conditions are imposed on a part of the strictly convex domain. In the second case, we impose the Dirichlet data on the boundary of a rectangle, an example of convex but not strictly convex domain. We show the existence of solutions and study their properties for particular cases of data.

Related

• The planar Least Gradient problem in convex domains
• The planar Least Gradient problem in convex domains: the discontinuous case
• The planar Least Gradient problem in convex domains, the case of continuous datum
• Least gradient problem with respect to a non-strictly convex norm
• Least gradient problem with Dirichlet condition imposed on a part of the boundary