Geodesic
On the validity of variational inequalities for obstacle problems with non-standard growth
Michela Eleuteri1 ; Antonia Passarelli di Napoli2
1 Università degli Studi di Modena E Reggio Emilia, Dipartimento di Scienze Fisiche, Informatiche e Matematiche
2 Università degli Studi di Napoli "Federico II", Dipartimento di Matematica e Applicazioni "R. Caccioppoli"
Annales Fennici Mathematici, Tome 47 (2022) no. 1, pp. 395-416.

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  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.  
DOI : 10.54330/afm.114655
Keywords: Variational inequalities, obstacle problems, duality formulas

Michela Eleuteri 1 ; Antonia Passarelli di Napoli 2

1 Università degli Studi di Modena E Reggio Emilia, Dipartimento di Scienze Fisiche, Informatiche e Matematiche
2 Università degli Studi di Napoli "Federico II", Dipartimento di Matematica e Applicazioni "R. Caccioppoli" 
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Michela Eleuteri; Antonia Passarelli di Napoli. On the validity of variational inequalities for obstacle problems with non-standard growth. Annales Fennici Mathematici, Tome 47 (2022) no. 1, pp. 395-416. doi : 10.54330/afm.114655. http://geodesic.mathdoc.fr/articles/10.54330/afm.114655/

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