Accepted Paper

Inserted: 31 jul 2026
Last Updated: 31 jul 2026

Journal: Annales Fennici Mathematici
Volume: 47
Number: 1
Pages: 395-416
Year: 2022
Doi: 10.54330/afm.114655

Abstract:

The aim of the paper is to show that the solutions to variational problems with non-standard growth conditions satisfy a corresponding variational inequality without any smallness assumptions on the gap between growth and coercitivity exponents. Our results rely on techniques based on Convex Analysis that consist in establishing duality formulas and pointwise relations between minimizers and corresponding dual maximizers, for suitable approximating problems, that are preserved passing to the limit. In this respect we are able to show that the right class of competitors are the functions with finite energy, in agreement with the unconstrained results.