DOI: 10.68381/jca18015 ISSN: 0944-6532
Existence of an Absolute Minimizer via Perron's Method
Vesa Julin
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))
F
(
u
,
Ω
)
=
ess sup
x
∈
Ω
f
(
x
,
u
(
x
)
,
D
u
(
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)].