(Non)uniqueness of minimizers in the least gradient problem
Wojciech G\'orny
TL;DR
This paper characterizes all minimizers in the least gradient problem with discontinuous boundary data, revealing their structural similarities and discussing stability of approximate solutions.
Contribution
It provides a complete characterization of minimizers and analyzes stability properties, addressing non-uniqueness issues in the least gradient problem.
Findings
Minimizers share similar level set structures.
Full characterization of the set of minimizers.
Stability properties of approximate solutions are discussed.
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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.