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Γ-Convergence of Inhomogeneous Functionals in Orlicz–Sobolev Spaces

Part of: Variational principles of physics Existence theories Linear function spaces and their duals

Published online by Cambridge University Press:  05 January 2015

Marian Bocea  and
Mihai Mihăilescu
Marian Bocea
Affiliation:
Department of Mathematics and Statistics, Loyola University Chicago, 1032 West Sheridan Road, Chicago, IL 60660, USA, ([email protected])
Mihai Mihăilescu
Affiliation:
Department of Mathematics, University of Craiova, 200585 Craiova, Romania, ([email protected]) ‘Simion Stoilow’ Institute of Mathematics of the Romanian Academy, PO Box 1-764, 014700 Bucharest, Romania
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Abstract

The asymptotic behaviour of inhomogeneous power-law type functionals is undertaken via De Giorgi’s Γ-convergence. Our results generalize recent work dealing with the asymptotic behaviour of power-law functionals acting on fields belonging to variable exponent Lebesgue and Sobolev spaces to the Orlicz–Sobolev setting.

Keywords

Γ-convergenceOrlicz–Sobolev spacesinhomogeneous power-law functionals

MSC classification

Primary: 46E30: Spaces of measurable functions ($L^p$-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
Secondary: 46E35: Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems 49J40: Variational methods including variational inequalities 49J45: Methods involving semicontinuity and convergence; relaxation 49S99: None of the above, but in this section
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 58 , Issue 2 , June 2015 , pp. 287 - 303
Copyright
Copyright © Edinburgh Mathematical Society 2015 

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