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Energy functional depending on elastic strain and chemical composition

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Abstract

In this paper we deal with energy functionals depending on elastic strain and chemical composition and we obtain lower semicontinuity results, existence theorems and relaxation in the spacesH 1,p(Ω; ℝn)×L q(Ω; ℝd) with respect to weak convergence. Our proofs use parametrized measures associated with weakly converging sequences.

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Authors and Affiliations

  1. Department of Mathematics, Carnegie Mellon University, 15213, Pittsburgh, PA, USA

    Irene Fonseca & David Kinderlehrer

  2. Departamento de Matematica Aplicada, Universidad Complutense de Madrid, 28040, Madrid, Spain

    Pablo Pedregal

Authors
  1. Irene Fonseca
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  2. David Kinderlehrer
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  3. Pablo Pedregal
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Additional information

The research was partially supported by the National Science Foundation under Grants No. DMS-9000133 and DMS-9201215 and also by the Army Research Office and the National Science Foundation through the Center for Nonlinear Analysis.

The research was partially supported by the National Science Foundation uncer Grants No. DMs 911572, the AFOSR 91 0301, the ARO DAAL03 92 G 003 and also by the ARO and the NSF through the Center for Nonlinear Analysis.

The research was supported by DGICYT (Spain) through “Programa de Perfeccionamiento y Movilidad del Personal Investigador” and through grant PB90-0245, by the Army Research Office and the National Science Foundation through the Center for Nonlinear Analysis and also by the project EurHomogenization SC1-CT91-0732 of the European Comunity.

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Fonseca, I., Kinderlehrer, D. & Pedregal, P. Energy functional depending on elastic strain and chemical composition. Calc. Var 2, 283–313 (1994). https://doi.org/10.1007/BF01235532

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