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Regularity for Double Phase Variational Problems

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Abstract

We prove sharp regularity theorems for minimisers of a class of variational integrals whose integrand switches between two different types of degenerate elliptic phases, according to the zero set of a modulating coefficient \({a(\cdot)}\). The model case is given by the functional

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

where q > p and \({a(\cdot) \geqq 0}\).

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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 Science 53/a, 43124, Parma, Italy

    Giuseppe Mingione

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

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Communicated by G. Dal Maso

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Colombo, M., Mingione, G. Regularity for Double Phase Variational Problems. Arch Rational Mech Anal 215, 443–496 (2015). https://doi.org/10.1007/s00205-014-0785-2

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  • DOI: https://doi.org/10.1007/s00205-014-0785-2

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