Geodesic
Existence of an Absolute Minimizer via Perron's Method
Journal of convex analysis, Tome 18 (2011) no. 1, pp. 277-284.

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The existence of an absolute minimizer for a functional \[ F(u,\Omega) = \underset{x \in \Omega}{ \text{ess sup}} \, f (x, u(x), Du(x)) \] is proved by using Perron's method. The function is assumed to be quasiconvex and uniformly coercive. This completes the result by T. Champion, L. De Pascale and F. Prinari [Gamma-convergence and absolute minimizers for supremal functionals, ESAIM Control Optim. Calc. Var. 10 (2004), No. 1, 14--27 (electronic)].
Classification : 49J45, 49J99
Mots-clés : Supremal functionals, absolute minimizer 
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     author = {V. Julin},
     title = {Existence of an {Absolute} {Minimizer} via {Perron's} {Method}},
     journal = {Journal of convex analysis},
     pages = {277--284},
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     number = {1},
     year = {2011},
     url = {http://geodesic.mathdoc.fr/item/JCA_2011_18_1_JCA_2011_18_1_a14/}
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V. Julin. Existence of an Absolute Minimizer via Perron's Method. Journal of convex analysis, Tome 18 (2011) no. 1, pp. 277-284. http://geodesic.mathdoc.fr/item/JCA_2011_18_1_JCA_2011_18_1_a14/