“A boundary monotonicity formula for almost-minimizers of the relative perimeter in nonsmooth domains”
Venerdì 12 Giugno 2026, ore 12:30 - Aula 2AB45 - Giacomo Vianello (UTIA - Czech Academy of Sciences)
Abstract
Monotonicity formulas for the renormalized perimeter in balls $B(x,r)$ play a central role in the regularity theory for minimizers and almost-minimizers of the relative perimeter in an open set $\Omega \subset \mathbb{R}^n$. For interior balls $B(x,r) \subset \Omega$, such formulas are classical. However, boundary monotonicity formulas typically rely on smoothness assumptions on the container.
In this talk, I will present a recent boundary monotonicity result that holds under a geometric visibility condition on $\Omega$ with respect to a point $x \in \partial\Omega$. This condition is satisfied by a large class of nonsmooth Lipschitz domains.
In the final part of the presentation, I will discuss how this formula can be applied to show that, up to subsequences, rescalings of the almost-minimizer converge to a minimizing cone contained in the tangent cone to $\Omega$ at $x$.
