Multiscale homogenization of integral convex functionals in Orlicz Sobolev setting

Joel Fotso Tachago; Giuliano Gargiulo; Hubert Nnang; Elvira Zappale

doi:10.3934/eect.2020067

Article Contents

2021, Volume 10, Issue 2: 297-320. Doi: 10.3934/eect.2020067

This issue Previous Article On the approximate controllability of neutral integro-differential inclusions of Sobolev-type with infinite delay Next Article Stabilization of the transmission wave/plate equation with variable coefficients on $ {\mathbb{R}}^n $

Multiscale homogenization of integral convex functionals in Orlicz Sobolev setting

1.
Higher Teacher, Training College Mathematics department. University of Bamenda, Faculty of Sciences, P.O. Box 39, Bambili, Cameroon
2.
Universitá degli Studi del Sannio, Dipartimento di Scienze e Tecnologie, Via De Sanctis, Benevento, 82100, Italy
3.
University of Yaounde I, École Normale Supérieure de Yaoundé, P.O. Box 47 Yaounde, Cameroon
4.
Dipartimento di Scienze di Base ed Applicate per l’Ingegneria, Sapienza Università di Roma, Via Antonio Scarpa, 16, 00161 Roma, Italy

^* Corresponding author: Elvira Zappale
^* Corresponding author: Elvira Zappale

Received: November 2019

Early access: June 23, 2020

Published online: June 23, 2020

The first and the last authors thank ICTP-INDAM Research in Pairs programme 2018

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Abstract

The $ \Gamma $-limit of a family of functionals $ u\mapsto \int_{\Omega }f\left( \frac{x}{\varepsilon },\frac{x}{\varepsilon ^{2}},D^{s}u\right) dx $ is obtained for $ s = 1,2 $ and when the integrand $ f = f\left( y,z,v\right) $ is a continous function, periodic in $ y $ and $ z $ and convex with respect to $ v $ with nonstandard growth. The reiterated two-scale limits of second order derivatives are characterized in this setting.

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Mathematics Subject Classification: Primary: 49J45, 46J10; Secondary: 46E30.

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References

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