Geodesic
Uniqueness and Continuous Dependence on Boundary Data for Integro-Extremal Minimizers of the Functional of the Gradient
Journal of convex analysis, Tome 14 (2007) no. 4, pp. 705-727.

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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. 
@article{JCA_2007_14_4_JCA_2007_14_4_a2,
     author = {S. Zagatti},
     title = {Uniqueness and {Continuous} {Dependence} on {Boundary} {Data} for {Integro-Extremal} {Minimizers} of the {Functional} of the {Gradient}},
     journal = {Journal of convex analysis},
     pages = {705--727},
     publisher = {mathdoc},
     volume = {14},
     number = {4},
     year = {2007},
     url = {http://geodesic.mathdoc.fr/item/JCA_2007_14_4_JCA_2007_14_4_a2/}
}
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S. Zagatti. Uniqueness and Continuous Dependence on Boundary Data for Integro-Extremal Minimizers of the Functional of the Gradient. Journal of convex analysis, Tome 14 (2007) no. 4, pp. 705-727. http://geodesic.mathdoc.fr/item/JCA_2007_14_4_JCA_2007_14_4_a2/