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Monotonicity formulas in linear and nonlinear potential theory

Presented by: 
Virginia Agostiniani Università degli Studi di Verona
Date: 
Wednesday 20th February 2019 - 16:00 to 17:00
Venue: 
INI Seminar Room 2
Abstract: 
In this talk, we rst recall how some monotonicity formulas can be derived along the level set ow of the capacitary potential associated with a given bounded domain. A careful analysis is required in order to preserve the monotonicity across the singular times, leading in turn to a new quantitative version of the Willmore inequality. Remarkably, such analysis can be carried out without any a priori knowledge of the size of the singular set. Hence, the same order of ideas applies to the p-capacitary potential of whose critical set, for p 6= 2, is not necessarily negligible. In this context, a generalised version of the Minkowski inequality is deduced.
Joint works with M. Fogagnolo and L. Mazzieri.

University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons