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Regularity Results for a Class of Functionals with Non-Standard Growth

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Abstract:

We consider the integral functional

under non-standard growth assumptions that we call p(x) type: namely, we assume that

a relevant model case being the functional

Under sharp assumptions on the continuous function p(x)>1 we prove regularity of minimizers. Energies exhibiting this growth appear in several models from mathematical physics.

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Authors and Affiliations

  1. Dipartimento di Matematica¶Università di Parma¶Via D'Azeglio 85/A¶43100 Parma (Italy)¶E-mail: acerbi@prmat.math.unipr.it¶E-mail: mingione@prmat.math.unipr.it, , , , , , IT

    Emilio Acerbi & Giuseppe Mingione

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  1. Emilio Acerbi
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  2. Giuseppe Mingione
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Accepted July 13, 2000¶Published online January 22, 2001

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Acerbi, E., Mingione, G. Regularity Results for a Class of Functionals with Non-Standard Growth. Arch. Rational Mech. Anal. 156, 121–140 (2001). https://doi.org/10.1007/s002050100117

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  • DOI: https://doi.org/10.1007/s002050100117

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