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

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Abstract

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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Authors and Affiliations

  1. Laboratoire MIPA, Université de Nîmes, Site des Carmes, Place Gabriel Péri, 30021, Nîmes, France

    Omar Anza Hafsa & Jean-Philippe Mandallena

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  1. Omar Anza Hafsa
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  2. Jean-Philippe Mandallena
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Correspondence to Omar Anza Hafsa.

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Communicated by J. Ball.

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Anza Hafsa, O., Mandallena, JP. Lower semicontinuity of integrals of the calculus of variations in Cheeger–Sobolev spaces. Calc. Var. 59, 53 (2020). https://doi.org/10.1007/s00526-020-1702-1

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