Branch points for (almost-)minimizers of two-phase free boundary problems. (5th January 2023)

• Record Type: Journal Article
• Authors: David, Guy; Engelstein, Max; Smit Vega Garcia, Mariana; Toro, Tatiana
• Is Part Of: Forum of mathematics. Volume 11(2023)
• Publication Date: 2023-01-05
• Subjects: 35R35; Mathematics -- Periodicals; 510
• DOI: 10.1017/fms.2022.105
• Languages: English
• ISSNs: 2050-5094

Abstract

Abstract: We study the existence and structure of branch points in two-phase free boundary problems. More precisely, we construct a family of minimizers to an Alt–Caffarelli–Friedman-type functional whose free boundaries contain branch points in the strict interior of the domain. We also give an example showing that branch points in the free boundary of almost-minimizers of the same functional can have very little structure. This last example stands in contrast with recent results of De Philippis, Spolaor and Velichkov on the structure of branch points in the free boundary of stationary solutions.