On the integral representation of variational functionals on $BD$

Marco Caroccia; Matteo Focardi; Nicolas Van Goethem

On the integral representation of variational functionals on $BD$

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arxiv 1907.11478 v2 pith:3I26YDWA submitted 2019-07-26 math.AP

Marco Caroccia , Matteo Focardi , Nicolas Van Goethem This is my paper · ORCID

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keywords functionalsintegralrepresentationvariationaladditionalassumptionsboundedclass

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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.

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Rigidity and functional properties of $\mathrm{BD}_{dev}(\Omega)$
math.AP 2025-05 accept novelty 8.0 of 10

The paper proves a rigidity structure theorem and computes an explicit kernel projection for maps of bounded deviatoric deformation in dimension n≥3, providing the main tools for relaxation and homogenization in BD_dev.

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