The aim of this paper is to deal with the asymptotics of generalized Orlicz norms when the lower growth rate tends to infinity. We generalize results proven by Bertazzoni, Harjulehto and Hasto in Journ. of Math. Anal. and Appl. (2024) for integral type energies (in generalized Orlicz spaces), considering milder convexity assumptions. Gamma-convergence results and related representation theorems in terms of L-infinity functionals are proven. The convexity hypotheses are completely removed in the variable exponent setting, thus extending the results in Eleuteri-Prinari in Nonlinear Anal. Real. World Appl. (2021) and Prinari-Zappale in JOTA (2020).
Approximation of $$L^\infty $$ functionals with generalized Orlicz norms / Bertazzoni, Giacomo; Eleuteri, Michela; Zappale, Elvira. - In: ANNALI DI MATEMATICA PURA ED APPLICATA. - ISSN 0373-3114. - (2024), pp. 1-22. [10.1007/s10231-024-01511-6]
Approximation of $$L^\infty $$ functionals with generalized Orlicz norms
Bertazzoni, Giacomo;Eleuteri, Michela;
2024
Abstract
The aim of this paper is to deal with the asymptotics of generalized Orlicz norms when the lower growth rate tends to infinity. We generalize results proven by Bertazzoni, Harjulehto and Hasto in Journ. of Math. Anal. and Appl. (2024) for integral type energies (in generalized Orlicz spaces), considering milder convexity assumptions. Gamma-convergence results and related representation theorems in terms of L-infinity functionals are proven. The convexity hypotheses are completely removed in the variable exponent setting, thus extending the results in Eleuteri-Prinari in Nonlinear Anal. Real. World Appl. (2021) and Prinari-Zappale in JOTA (2020).
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