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Second-Order Structured Deformations in the Space of Functions of Bounded Hessian

  • Irene Fonseca
  • Adrian Hagerty
  • Roberto ParoniEmail author
Article
  • 6 Downloads

Abstract

This work addresses second-order structured deformations in the framework of the space of special functions of bounded Hessian, BH. An integral representation result is obtained in BH in the vein of the global method for relaxation of Bouchitté et al. (Arch. Ration. Mech. Anal. 145:51–98, 1998) and is applied to a relaxation problem in the context of structured deformations.

Keywords

Relaxation Lower semicontinuity Second-order structured deformations Functions of bounded Hessian 

Mathematics Subject Classification

49J45 49S05 74Q99 

Notes

Acknowledgements

This paper is part of the A. Hagerty’s Ph.D. thesis at Carnegie Mellon University. The authors acknowledge the Center for Nonlinear Analysis where part of this work was carried out. The research of I. Fonseca was partially funded by the National Science Foundation under Grant No. DMS-1411646. The research of A. Hagerty was partially funded by National Science Foundation under PIRE Grant Nos. OISE-0967140 and DMS-1411646. The research of R. Paroni was partially funded from the Università di Pisa through the Grant PRA_2018_61.

References

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Mathematical SciencesCarnegie Mellon UniversityPittsburghUSA
  2. 2.Dipartimento di Ingegneria Civile e IndustrialeUniversità di PisaPisaItaly

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