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Journal of Convex Analysis 28 (2021), No. 2, 569--580
Copyright Heldermann Verlag 2021



Duality Arguments for Linear Elasticity Problems with Incompatible Deformation Fields

Adriana Garroni
Dip. di Matematica "G. Castelnuovo", Sapienza UniversitÓ, Roma, Italy
garroni@mat.uniroma1.it

Annalisa Malusa
Dip. di Matematica "G. Castelnuovo", Sapienza UniversitÓ, Roma, Italy
malusa@mat.uniroma1.it



We prove existence and uniqueness for solutions to equilibrium problems for free-standing, traction-free, non homogeneous crystals in the presence of plastic slips. Moreover we prove that this class of problems is closed under G-convergence of the operators. In particular the homogenization procedure, valid for elliptic systems in linear elasticity, depicts the macroscopic features of a composite material in the presence of plastic deformation.

Keywords: Boundary value problems for elliptic systems, elastic problems, duality solutions, homogenization.

MSC: 35D30; 35J58.

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