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Local Lipschitz continuity for energy integrals with slow growth

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Abstract

We consider some energy integrals under slow growth, and we prove that the local minimizers are locally Lipschitz continuous. Many examples are given, either with subquadratic \(p,q-\)growth and/or anisotropic growth.

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Authors and Affiliations

  1. Dipartimento di Scienze Fisiche, Informatiche e Matematiche, Università degli Studi di Modena e Reggio Emilia, via Campi 213/b, 41125, Modena, Italy

    Michela Eleuteri & Stefania Perrotta

  2. Dipartimento di Matematica e Informatica “U. Dini”, Università di Firenze, Viale Morgagni 67/A, 50134, Firenze, Italy

    Paolo Marcellini & Elvira Mascolo

Authors
  1. Michela Eleuteri
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  2. Paolo Marcellini
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  3. Elvira Mascolo
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  4. Stefania Perrotta
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Correspondence to Paolo Marcellini.

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The authors are members of GNAMPA (Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni) of INdAM (Istituto Nazionale di Alta Matematica).

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Eleuteri, M., Marcellini, P., Mascolo, E. et al. Local Lipschitz continuity for energy integrals with slow growth. Annali di Matematica 201, 1005–1032 (2022). https://doi.org/10.1007/s10231-021-01147-w

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  • DOI: https://doi.org/10.1007/s10231-021-01147-w

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