(Non)uniqueness of minimizers in the least gradient problem

2017/09/07 by Górny, Wojciech
#35J20 #35J25 #35J75 #35J92 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1709.02185

Abstract

Minimizers in the least gradient problem with discontinuous boundary data need not be unique. However, all of them have a similar structure of level sets. Here, we give a full characterization of the set of minimizers in terms of any one of them and discuss stability properties of an approximate problem.

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