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.File | Dimensione | Formato | |
---|---|---|---|
Foc_Gel_Pis_published.pdf
Accesso chiuso
Tipologia:
Versione finale referata (Postprint, Accepted manuscript)
Licenza:
Tutti i diritti riservati
Dimensione
235.66 kB
Formato
Adobe PDF
|
235.66 kB | Adobe PDF | Richiedi una copia |
I documenti in FLORE sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.