Year: 2023
Type: preprint
Abstract: In this paper, we investigate Bernoulli type free boundary problem on collapsed RCD(K,N)-spaces. We prove the existence of minimizers and prove the local Lipschitz continuity of minimizers provided that the negative part is locally Lipschitz continuous. In particular, we prove the local Lipschitz continuity of minimizers for the one-phase problem (i.e. when the solution is non-negative). And then we prove that the free boundaries of minimizers have locally finite perimeter. We emphasize that the proof in this paper applies to collapsed RCD(K,N)-spaces and does not rely on the non-collapsed condition.
Source: arXiv (Cornell University)
Author: Lin, Sitan
Institution: Shanghai Jiao Tong University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4366400523