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 [1]. 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 problem in the plane
GELLI, MARIA STELLA;
2010-01-01
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 [H^1] ) and satisfying an indecomposability constraint (according to the definition by [1]. 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 in questo prodotto:
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