Journal Home Page Cumulative Index List of all Volumes Complete Contentsof this Volume Previous Article Journal of Convex Analysis 18 (2011), No. 1, 277--284Copyright 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 vesa.julin@jyu.fi [Abstract-pdf] 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 [ Fulltext-pdf  (115  KB)] for subscribers only.