TY - JOUR T1 - The sharp quantitative isocapacitary inequality JF - Revista Matematica Iberoamericana Y1 - 2021 A1 - Guido De Philippis A1 - Michele Marini A1 - Ekaterina Mukoseeva KW - Fraenkel asymmetry KW - isocapacitary inequality KW - Stability estimates AB -

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

VL - 37 SN - 02132230 (ISSN) UR - https://www.scopus.com/inward/record.uri?eid=2-s2.0-85104691573&doi=10.4171%2frmi%2f1259&partnerID=40&md5=5f88bc37b87a9eea7a502ea63523ff57 IS - 6 JO - Rev. Mat. Iberoam. ER - TY - JOUR T1 - The sharp quantitative isocapacitary inequality (the case of p-capacity) JF - Advances in Calculus of Variations Y1 - 2021 A1 - Ekaterina Mukoseeva KW - isocapacitary inequality KW - Stability estimates AB -

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.

SN - 18648258 (ISSN) UR - https://www.scopus.com/inward/record.uri?eid=2-s2.0-85106363307&doi=10.1515%2facv-2020-0106&partnerID=40&md5=26dbcad781b68c1d873512e272f0e7f4 JO - Adv. Calc. Var. ER - TY - ABST T1 - Minimality of the ball for a model of charged liquid droplets Y1 - 2020 A1 - Ekaterina Mukoseeva A1 - Giulia Vescovo ER -