Carleman estimates for stationary $Q$-valued maps: a variational approach
Aria Halavati, Luca Spolaor
TL;DR
This paper establishes a Carleman estimate for stationary multivalued functions and uses it to reprove the optimal dimension of their singular set, offering a new variational approach.
Contribution
It introduces a novel Carleman estimate for Dirichlet-stationary multivalued functions and applies it to analyze the singular set dimension.
Findings
Proved a Carleman estimate for multivalued functions
Provided a new proof for the singular set dimension
Enhanced understanding of Dir-minimizing multivalued functions
Abstract
We prove a Carleman-type estimate for Dirichlet-stationary multivalued functions and apply it to give a different proof of the optimal dimension of the singular set of Dir-minimizing multivalued functions, originally due to Almgren and to De Lellis-Spadaro.
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.
Taxonomy
TopicsAdvanced Mathematical Modeling in Engineering · Nonlinear Partial Differential Equations · Stability and Controllability of Differential Equations