We prove an Allard-type regularity theorem for free-boundary minimal surfaces in Lipschitz domains locally modeled on convex polyhedra. We show that if such a minimal surface is sufficiently close to an appropriate free-boundary plane, then the surface is (Formula presented.) graphical over this plane. We apply our theorem to prove partial regularity results for free-boundary minimizing hypersurfaces, and relative isoperimetric regions.
|Original language||English (US)|
|Number of pages||62|
|Journal||Communications on Pure and Applied Mathematics|
|State||Published - May 2022|
ASJC Scopus subject areas
- Applied Mathematics