Existence of an absolute minimizer via Perron's method

preprint2010arXivOpen access

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.

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Existence of an absolute minimizer via Perron's method

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