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Relaxation of p-Growth Integral Functionals Under Space-Dependent Differential Constraints

  • Elisa DavoliEmail author
  • Irene Fonseca
Chapter
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Part of the Springer INdAM Series book series (SINDAMS, volume 27)

Abstract

A representation formula for the relaxation of integral energies
$$\displaystyle (u,v)\mapsto \int _\varOmega f(x,u(x),v(x))\,dx, $$
is obtained, where f satisfies p-growth assumptions, 1 < p < +, and the fields v are subjected to space-dependent first order linear differential constraints in the framework of \(\mathcal {A}\)-quasiconvexity with variable coefficients.

Notes

Acknowledgements

The authors thank the Center for Nonlinear Analysis (NSF Grant No. DMS-0635983), where this research was carried out, and also acknowledge support of the National Science Foundation under the PIRE Grant No. OISE-0967140. The research of I. Fonseca and E. Davoli was funded by the National Science Foundation under Grant No. DMS- 0905778. E. Davoli acknowledges the support of the Austrian Science Fund (FWF) projects P 27052 and I 2375. The research of I. Fonseca was further partially supported by the National Science Foundation under Grant No. DMS-1411646.

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Faculty of MathematicsUniversity of ViennaViennaAustria
  2. 2.Department of MathematicsCarnegie Mellon UniversityPittsburghUSA

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