The behavior of an almost-minimizer of the relative perimeter near a boundary vertex of the container.

Abstract: It is known that the boundary of an almost-minimizer of the relative perimeter inside a smooth container satisfies Young's Law, namely, it meets the container boundary orthogonally. Much less is known when the container is nonsmooth. In this talk, I will describe some recent results concerning the behavior of an almost-minimizer of the relative perimeter near an isolated singularity (vertex) of its container boundary. I will show that, in dimension three, a phenomenon we call vertex-skipping occurs, that is, the boundary of an almost-minimizer cannot pass through a vertex of its container, while in higher dimensions the situation is more intricate, and a relation between the "aperture" of the vertex and the avoidance of the singularity emerges. I will conclude by discussing some related open questions. This is part of a joint project with Gian Paolo Leonardi (University of Trento).

MathematicsPhysics

Audience: researchers in the topic

Nečas Seminar on Continuum Mechanics

Series comments: This seminar was founded on December 14, 1966.

Faculty of Mathematics and Physics, Charles University, Sokolovská 83, Prague 8. If not written otherwise, we will meet on Mondays at 15:40 in lecture hall K3 (2nd floor)