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.
2001
Buttazzo, Giuseppe; DE PASCALE, Luigi; Fragala', I.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11568/186379
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