Second-Order Structured Deformations in the Space of Functions of Bounded Hessian
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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.
KeywordsRelaxation Lower semicontinuity Second-order structured deformations Functions of bounded Hessian
Mathematics Subject Classification49J45 49S05 74Q99
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.
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