Speaker: Marco Caroccia (Università degli studi di Roma Tor Vergata).

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.

Zoom: https://videoconf-colibri.zoom.us/j/81421184299 | Online access password: lisbonwade

The Lisbon Webinar in Analysis in Differential Equations is a joint iniciative of CAMGSD, CMAFcIO and GFM, three research centers of the University of Lisbon. It is aimed at filling the absence of face-to-face seminars and wishes to be a meeting point of mathematicians working in the field.