Existence of an absolute minimizer via Perron's method
arXiv:1004.5008
Abstract
In this paper the existence of an absolute minimizer for a functional \[ F(u,Ω) = \underset{x \in Ω}{\text{ess sup}} \, f (x, u(x), Du(x)) \] is proved by using Perron's method. The function is assumed to be quasiconvex and uniformly coercive. This completes the result by Champion, De Pascale and Prinari.