Inserted: 13 apr 2000
Last Updated: 10 dec 2003
Journal: Discrete Contin. Dinam. Systems
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.