Accepted Paper

Inserted: 31 jul 2026
Last Updated: 31 jul 2026

Journal: Annali di Matematica Pura ed Applicata
Volume: 204
Number: (3)
Pages: 903–924
Year: 2025

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 Hästö in Journ. of Math. Anal. and Appl. (2024) for integral type energies (in generalized Orlicz spaces), considering milder convexity assumptions.\color{black} $\Gamma$-convergence results and related representation theorems in terms of $L^\infty$ functionals are proven.%for sequences of generalized Orlicz energies under mild convexity assumptions. 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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