%0 Journal Article %J Revista Matematica Iberoamericana %D 2021 %T The sharp quantitative isocapacitary inequality %A Guido De Philippis %A Michele Marini %A Ekaterina Mukoseeva %K Fraenkel asymmetry %K isocapacitary inequality %K Stability estimates %X

We prove a sharp quantitative form of the classical isocapacitary inequality. Namely, we show that the difference between the capacity of a set and that of a ball with the same volume bounds the square of the Fraenkel asymmetry of the set. This provides a positive answer to a conjecture of Hall, Hayman, and Weitsman (J. Analyse Math.'91). © 2021 Real Sociedad Matemática Española

%B Revista Matematica Iberoamericana %V 37 %P 2191 - 2228 %8 2021 %@ 02132230 (ISSN) %G eng %U https://www.scopus.com/inward/record.uri?eid=2-s2.0-85104691573&doi=10.4171%2frmi%2f1259&partnerID=40&md5=5f88bc37b87a9eea7a502ea63523ff57 %N 6 %! Rev. Mat. Iberoam. %0 Journal Article %J Advances in Calculus of Variations %D 2021 %T The sharp quantitative isocapacitary inequality (the case of p-capacity) %A Ekaterina Mukoseeva %K isocapacitary inequality %K Stability estimates %X

We prove a sharp quantitative form of isocapacitary inequality in the case of a general p. This work is a generalization of the author's paper with Guido De Philippis and Michele Marini, where we treated the case of 2-capacity. © 2021 Walter de Gruyter GmbH, Berlin/Boston 2021.

%B Advances in Calculus of Variations %8 2021 %@ 18648258 (ISSN) %G eng %U https://www.scopus.com/inward/record.uri?eid=2-s2.0-85106363307&doi=10.1515%2facv-2020-0106&partnerID=40&md5=26dbcad781b68c1d873512e272f0e7f4 %! Adv. Calc. Var. %0 Generic %D 2020 %T Minimality of the ball for a model of charged liquid droplets %A Ekaterina Mukoseeva %A Giulia Vescovo %G eng