Calculus of Variations and Geometric Measure Theory

G. Buttazzo - L. De Pascale - I. FragalĂ 

Topological Equivalence of Some Variational Problems Involving Distances

created on 13 Apr 2000
modified on 10 Dec 2003


Published Paper

Inserted: 13 apr 2000
Last Updated: 10 dec 2003

Journal: Discrete Contin. Dinam. Systems
Volume: 7
Pages: 247-258
Year: 2001


To every distance $d$ on a given open set $\Omega \subset \R ^n$, we may associate several kinds of variational problems. We show that, on the class of all geodesic distances $d$ on $\Omega$ which are bounded from above and from below by fixed multiples of the Euclidean one, the uniform convergence on compact sets turns out to be equivalent to the $\Gamma$-convergence of each of the corresponding variational problems under consideration.