Following the global method for relaxation we prove an integral representation result for a large class of variational functionals naturally defined on the space of functions with Bounded Deformation. Mild additional continuity assumptions are required on the functionals. The result is applied to investigate the lower semicontinuity, the relaxation and the homogenization of bulk (and surface) energies defined on BD.
On the integral representation of variational functionals on BD / Marco Caroccia, Matteo Focardi, Nicolas Van Goethem. - In: SIAM JOURNAL ON MATHEMATICAL ANALYSIS. - ISSN 0036-1410. - STAMPA. - 52:(2020), pp. 422-467. [10.1137/19M1277564]
On the integral representation of variational functionals on BD
Matteo Focardi
;
2020
Abstract
Following the global method for relaxation we prove an integral representation result for a large class of variational functionals naturally defined on the space of functions with Bounded Deformation. Mild additional continuity assumptions are required on the functionals. The result is applied to investigate the lower semicontinuity, the relaxation and the homogenization of bulk (and surface) energies defined on BD.
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