Opuscula Math. 39, no. 2 (2019), 259-279

Opuscula Mathematica

Isotropic and anisotropic double-phase problems: old and new

Vicenţiu D. Rădulescu

Abstract. We are concerned with the study of two classes of nonlinear problems driven by differential operators with unbalanced growth, which generalize the \((p,q)\)- and \((p(x),q(x))\)-Laplace operators. The associated energy is a double-phase functional, either isotropic or anisotropic. The content of this paper is in relationship with pioneering contributions due to P. Marcellini and G. Mingione.

Keywords: differential operator with unbalanced growth, double-phase energy, variable exponent.

Mathematics Subject Classification: 35J60, 35J65, 58E05.

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  • Vicenţiu D. Rădulescu
  • ORCID iD https://orcid.org/0000-0003-4615-5537
  • AGH University of Science and Technology, Faculty of Applied Mathematics, al. Mickiewicza 30, 30-059 Kraków, Poland
  • Institute of Mathematics, Physics and Mechanics, Jadranska 19, 1000 Ljubljana, Slovenia
  • Institute of Mathematics "Simion Stoilow", Romanian Academy of Sciences, P.O. Box 1-764, 014700 Bucharest, Romania
  • Communicated by Dušan Repovš.
  • Received: 2018-11-04.
  • Accepted: 2018-11-10.
  • Published online: 2018-12-07.
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Cite this article as:
Vicenţiu D. Rădulescu, Isotropic and anisotropic double-phase problems: old and new, Opuscula Math. 39, no. 2 (2019), 259-279, https://doi.org/10.7494/OpMath.2019.39.2.259

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