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

Marco Caroccia (Università degli studi di Roma Tor Vergata - Dipartimento di Matematica)

created by vangoeth on 17 Nov 2020

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

WADE (Webinar in Analysis and Differential Equations)

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, 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 and with a brief explanation of its connection with the Diri chlet (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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