Double phase problems: a survey of some recent results

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