English

Existence of an absolute minimizer via Perron's method

Analysis of PDEs 2015-03-17 v1

Abstract

In this paper the existence of an absolute minimizer for a functional F(u,Ω)=ess supxΩf(x,u(x),Du(x)) 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 Champion, De Pascale and Prinari.

Keywords

Cite

@article{arxiv.1004.5008,
  title  = {Existence of an absolute minimizer via Perron's method},
  author = {Vesa Julin},
  journal= {arXiv preprint arXiv:1004.5008},
  year   = {2015}
}