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Journal of Convex Analysis 18 (2011), No. 1, 277--284
Copyright Heldermann Verlag 2011

Existence of an Absolute Minimizer via Perron's Method

Vesa Julin
Dept. of Mathematics and Statistics, P. O. Box 35, University of Jyväskylä, 40014 Jyväskylä, Finland


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)].

Keywords: Supremal functionals, absolute minimizer.

MSC: 49J45, 49J99

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