In this paper, we prove that the Lp approximants naturally associated to a supremal functional Gamma-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) among these minimizers. We provide two different proofs of this fact relying on different assumptions and techniques.
Gamma-convergence and Absolute Minimizers for Supremal Functionals / CHAMPION T; DE PASCALE L; PRINARI F. - In: ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS. - ISSN 1262-3377. - STAMPA. - 10:1(2004), pp. 14-27. [10.1051/cocv:2003036]
Gamma-convergence and Absolute Minimizers for Supremal Functionals
DE PASCALE, LUIGI;
2004
Abstract
In this paper, we prove that the Lp approximants naturally associated to a supremal functional Gamma-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) among these minimizers. We provide two different proofs of this fact relying on different assumptions and techniques.File | Dimensione | Formato | |
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