Approximation of $L^\infty$ functionals with generalized Orlicz norms

TL;DR

This paper investigates the asymptotic behavior of generalized Orlicz norms as their lower growth rate approaches infinity, establishing $ ext{Gamma}$-convergence and representation theorems for $L^00$ functionals, with extensions to variable exponent cases.

Contribution

It provides new $ ext{Gamma}$-convergence results for generalized Orlicz energies and removes convexity assumptions in the variable exponent setting.

Findings

$ ext{Gamma}$-convergence of generalized Orlicz norms to $L^00$ functionals

Representation theorems for the asymptotic limits

Extension of results to variable exponent Orlicz spaces

Abstract

The aim of this paper is to deal with the asymptotics of generalized Orlicz norms when the lower growth rate tends to infinity. $\Gamma$-convergence results and related representation theorems in terms of $L^\infty$ functionals are proven for sequences of generalized Orlicz energies under mild convexity assumptions. This latter hypothesis is removed in the variable exponent setting.