We study a $1$-capacitary type problem in $\R^2$: given a set $E$, we minimize the perimeter (in the sense of De Giorgi) among all the sets containing $E$ (modulo $\Huno$) and satisfying an indecomposability constraint (according to the definition by Ambrosio-Caselles-Masnou-Morel). By suitably choosing the representant of the relevant set $E$, we show that a convexification process characterizes the minimizers. As a consequence of our result we determine the $1$-capacity of (a suitable representant of) sets with finite perimeter in the plane.

On a 1-capacitary type problem in the plane / M. Focardi; M.S. Gelli; G. Pisante. - In: COMMUNICATIONS ON PURE AND APPLIED ANALYSIS. - ISSN 1534-0392. - STAMPA. - 9(2010), pp. 1319-1334. [10.3934/cpaa.2010.9.1319]

On a 1-capacitary type problem in the plane

FOCARDI, MATTEO;
2010

Abstract

We study a $1$-capacitary type problem in $\R^2$: given a set $E$, we minimize the perimeter (in the sense of De Giorgi) among all the sets containing $E$ (modulo $\Huno$) and satisfying an indecomposability constraint (according to the definition by Ambrosio-Caselles-Masnou-Morel). By suitably choosing the representant of the relevant set $E$, we show that a convexification process characterizes the minimizers. As a consequence of our result we determine the $1$-capacity of (a suitable representant of) sets with finite perimeter in the plane.
9
1319
1334
M. Focardi; M.S. Gelli; G. Pisante
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2158/394219
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