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arXiv:2009.04048 [math.AP]AbstractReferencesReviewsResources

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

Wojciech Górny

Published 2020-09-09Version 1

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.

Comments: 22 pages, 4 figures
Categories: math.AP
Subjects: 35J20, 35J25, 35J75, 35J92
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