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Article Dans Une Revue Calculus of Variations and Partial Differential Equations Année : 2020

Lower semicontinuity of integrals of the calculus of variations in Cheeger-Sobolev spaces

Résumé

A necessary condition called $H_\mu^{1,p}$-quasiconvexity on $p$-coercive integrands is introduced for the lower semicontinuity with respect to the strong convergence of $L^p_\mu(X;{\mathbb R}^m)$ of integral functionals defined on Cheeger-Sobolev spaces. Under polynomial growth conditions it turns out that this condition is necessary and sufficient.
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Dates et versions

hal-02295885 , version 1 (24-09-2019)

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Omar Anza Hafsa, Jean Philippe Mandallena. Lower semicontinuity of integrals of the calculus of variations in Cheeger-Sobolev spaces. Calculus of Variations and Partial Differential Equations, 2020, 59 (2), ⟨10.1007/s00526-020-1702-1⟩. ⟨hal-02295885⟩

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