Opuscula Math. 42, no. 2 (2022), 257-278
https://doi.org/10.7494/OpMath.2022.42.2.257

 
Opuscula Mathematica

Double phase problems: a survey of some recent results

Nikolaos S. Papageorgiou

Abstract. We review some recent results on double phase problems. We focus on the relevant function space framework, which is provided by the generalized Orlicz spaces. We also describe the basic tools and methods used to deal with double phase problems, given that there is no global regularity theory for these problems.

Keywords: double phase integrand, generalized Orlicz spaces, regularity theory, maximum principle, Nehari manifold.

Mathematics Subject Classification: 35J20, 35J60.

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  • Nikolaos S. Papageorgiou
  • National Technical University, Department of Mathematics, Zografou Campus, Athens 15780, Greece
  • Communicated by Vicentiu D. Rădulescu.
  • Received: 2022-01-18.
  • Accepted: 2022-02-01.
  • Published online: 2022-02-25.
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Cite this article as:
Nikolaos S. Papageorgiou, Double phase problems: a survey of some recent results, Opuscula Math. 42, no. 2 (2022), 257-278, https://doi.org/10.7494/OpMath.2022.42.2.257

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