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Journal of Convex Analysis 14 (2007), No. 4, 705--727
Copyright Heldermann Verlag 2007

Uniqueness and Continuous Dependence on Boundary Data for Integro-Extremal Minimizers of the Functional of the Gradient

Sandro Zagatti
S.I.S.S.A., Via Beirut 2/4, 34014 Trieste, Italy

We study some qualitative properties of the integro-extremal minimizers of the functional of the gradient defined on Sobolev spaces with Dirichlet boundary conditions. We discuss their use in the non-convex case via viscosity methods and give conditions under which they are unique and depend continuously on boundary data.

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