Matteo Focardi - Dipartimento di Matematica "U. Dini", Università di Firenze, viale Morgagni 67/A, I-50139 Firenze, Italy (email)
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 $H^1$) and
satisfying an indecomposability constraint
(according to the definition by .
By suitably choosing the representant of the relevant set $E$,
we show that a convexification process characterizes the minimizers.
Keywords: Perimeter, capacity, indecomposable sets.
Received: August 2009; Revised: December 2009; Published: May 2010.
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