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Monotonicity formulas in linear and nonlinear potential theory

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DNM - The mathematical design of new materials

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.

This talk is part of the Isaac Newton Institute Seminar Series series.

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