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).
The sharp quantitative isocapacitary inequality / de Philippis, G.; Marini, M.; Mukoseeva, E.. - In: REVISTA MATEMATICA IBEROAMERICANA. - ISSN 0213-2230. - 37:6(2021), pp. 2191-2228. [10.4171/rmi/1259]
The sharp quantitative isocapacitary inequality
de Philippis G.;Mukoseeva E.
2021-01-01
Abstract
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).File in questo prodotto:
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