Open AccessOn the validity of variational inequalities for obstacle problems with non-standard growth
Author(s) -
Michela Eleuteri,
Antonia Passarelli di Napoli
Publication year - 2022
Publication title -
annales fennici mathematici
Language(s) - English
Resource type - Journals
eISSN - 2737-114X
pISSN - 2737-0690
DOI - 10.54330/afm.114655
Subject(s) - pointwise , variational inequality , obstacle , limit (mathematics) , mathematics , duality (order theory) , obstacle problem , regular polygon , variational analysis , inequality , zero (linguistics) , mathematical analysis , mathematical optimization , pure mathematics , geometry , political science , law , linguistics , philosophy
The aim of the paper is to show that the solutions to variational problems with non-standard growth conditions satisfy a corresponding variational inequality expressed in terms of a duality formula between the constrained minimizers and the corresponding dual maximizers, 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 pointwise relations that are preserved passing to the limit. We point out that we are able to deal with very general obstacle quasi-continuous up to a subset of zero capacity.