We study a 1-capacitary type problem in the plane. Qiven a set , we minimize the perimeter (in the sense of De Giorgi) among all the sets containing (modulo H^1) and satisfying an indecomposability constraint. By suitably choosing the representant of the relevant set, 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
PISANTE, Giovanni
2010
Abstract
We study a 1-capacitary type problem in the plane. Qiven a set , we minimize the perimeter (in the sense of De Giorgi) among all the sets containing (modulo H^1) and satisfying an indecomposability constraint. By suitably choosing the representant of the relevant set, 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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