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.

On the validity of variational inequalities for obstacle problems with non-standard growth / Eleuteri, M.; di Napoli, A. P.. - In: ANNALES FENNICI MATHEMATICI. - ISSN 2737-0690. - 47:1(2022), pp. 395-416. [10.54330/afm.114655]

On the validity of variational inequalities for obstacle problems with non-standard growth

Eleuteri M.;
2022

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 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.
2022
47
1
395
416
On the validity of variational inequalities for obstacle problems with non-standard growth / Eleuteri, M.; di Napoli, A. P.. - In: ANNALES FENNICI MATHEMATICI. - ISSN 2737-0690. - 47:1(2022), pp. 395-416. [10.54330/afm.114655]
Eleuteri, M.; di Napoli, A. P.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11380/1270189
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