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Free-boundary regularity for almost-minimizers in non-smooth domains

by Prof. Gian Paolo Leonardi

This is my image.
This is my image.
This is my image.

11:00-12:00 Thursday, 3 April 2025
Auditorium, Rectorate



Abstract

While interior regularity theory for almost-minimizers of the perimeter functional has been established since 1984, much less is known about the boundary behavior even of full minimizers of the relative perimeter, when the boundary of the container is not smooth enough. Our aim is to develop tools for studying the boundary regularity problem in non-smooth settings. Our first result is a monotonicity formula proved when the container satisfies a so-called visibility property from a given boundary point. Then, we show that almost-minimizers in 3-dimensional convex containers always “skip” the vertices of the container, while this is false in dimension 5 and higher. This is a joint collaboration with Giacomo Vianello (University of Padova).