To every distance d on a given open set \Omega\subseteq\mathbb 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.
Topological equivalence of some variational problem associated to distances
BUTTAZZO, GIUSEPPE;DE PASCALE, LUIGI;
2001-01-01
Abstract
To every distance d on a given open set \Omega\subseteq\mathbb 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.File in questo prodotto:
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