Regularity and Dirichlet problem for double-phase energy functionals of different power growth. (English) Zbl 1534.35059
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.
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.
Reviewer: Maria Alessandra Ragusa (Catania)
MSC:
| 35B65 | Smoothness and regularity of solutions to PDEs |
| 35J62 | Quasilinear elliptic equations |
| 35J92 | Quasilinear elliptic equations with \(p\)-Laplacian |
| 35J25 | Boundary value problems for second-order elliptic equations |
Keywords:
double-phase energy functional; embedding results; generalized Orlicz space; non-standard power growthReferences:
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