Calculus of Variations and Geometric Measure Theory

S. J. N. Mosconi - P. Tilli

$\Gamma$-convergence for the irrigation problem

created on 24 Jan 2003
modified on 27 May 2003


Accepted Paper

Inserted: 24 jan 2003
Last Updated: 27 may 2003

Year: 2003


In this paper we study the asymptotics of the functional $F(\gamma)=\int f(x) d_\gamma(x)^pdx$, where $d_\gamma$ is the distance function to $\gamma$, among all connected compact sets $\gamma$ of given length, when the prescribed length tends to infinity. After properly scaling, we prove the existence of a $\Gamma$-limit in the space of probability measures, thus retrieving information on the asymptotics of minimal sequences.