Regularity and Dirichlet problem for double-phase energy functionals of different power growth (Q6123472)

The authors study properties of the new double-phase differential operator in the context of Musielak-Orlicz spaces, focusing on the embeddings results. They obtain existence and uniqueness of weak solutions to certain Dirichlet double-phase problems with both uncontrolled and controlled growth of the reaction term. The main features of these problems are the presence of a logarithmic perturbation in the principal operator and the reaction that may exhibit the effects of convection.