Calculus of Variations and Geometric Measure Theory
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Contact surface of Cheeger sets

Marco Caroccia (Dipartimento di Matematica, Politecnico di Milano)

created on 17 Nov 2020
modified on 26 Nov 2020

26 nov 2020 -- 15:30   [open in google calendar]

WADE (Webinar in Analysis and Differential Equations)--Paris time

Abstract.

Geometrical properties of Cheeger sets have been deeply studied by many authors since their introduction, as a way of bounding from below the first Dirichlet (p)-Laplacian eigenvualue. They represents the first eigenfunction of the Dirichlet (1)-Laplacian of a domain. In this talk we will introduce a recent property, studied in collaboration with Simone Ciani (Università degli studi di Firenze), concerning their contact surface with the ambient space. In particular we will show that the contact surface cannot be too small, with a lower bound on the dimension strictly related to the regularity of the ambient space. The talk will focus on the introduction of the problem. It will start with a brief explanation of its connection with the Dirichlet (p)-Laplacian eigenvalue problem. Then a brief sketch of the proof is given. Functional to the whole argument is the notion of removable singularity, as a tool for extending solutions of pdes under some regularity constraint.

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