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Bounded Minimisers of Double Phase Variational Integrals

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Abstract

Bounded minimisers of the functional

$$w \mapsto \int (|Dw|^p+a(x)|Dw|^q)\,{\rm d}x,$$

where \({0 \leqq a(\cdot) \in C^{0, \alpha}}\) and \({1 < p < q}\), are \({C^{1, \beta}}\)-regular provided the sharp bound \({q \leqq p + \alpha}\) holds.

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Authors and Affiliations

  1. Scuola Normale Superiore di Pisa, p.za dei Cavalieri, 7, 56126, Pisa, Italy

    Maria Colombo

  2. Dipartimento di Matematica e Informatica, Università di Parma, Parco Area delle Scienze 53/a, 43124, Parma, Italy

    Giuseppe Mingione

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  1. Maria Colombo
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  2. Giuseppe Mingione
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Correspondence to Giuseppe Mingione.

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Communicated by C. De Lellis

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Colombo, M., Mingione, G. Bounded Minimisers of Double Phase Variational Integrals. Arch Rational Mech Anal 218, 219–273 (2015). https://doi.org/10.1007/s00205-015-0859-9

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