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In this paper, we prove that the approximants naturally associated to a supremal functional -converge to it. This yields a lower semicontinuity result for supremal functionals whose supremand satisfy weak coercivity assumptions as well as a generalized Jensen inequality. The existence of minimizers for variational problems involving such functionals (together with a Dirichlet condition) then easily follows. In the scalar case we show the existence of at least one absolute minimizer (i.e. local...
In this paper, we prove that the Lp approximants naturally associated to a supremal functional
Γ-converge to it. This yields a lower semicontinuity result for supremal
functionals whose supremand satisfy weak coercivity assumptions as
well as a generalized Jensen inequality. The existence of minimizers
for variational problems involving such functionals (together with a
Dirichlet condition) then easily follows. In the scalar
case we show the existence of at least one absolute minimizer (i.e. local
solution)...
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