Existence of an absolute minimizer via Perron's method

Details Existence of an absolute minimizer via Perron's method Existence of an absolute minimizer via Perron's method

2010-04-28

arxiv.org/abs/1004.5008v1

Mathematics

Analysis of PDEs

Scientific paper

In this paper 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 Champion, De Pascale and
Prinari.

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