Embedding and extension results in fractional Musielak–Sobolev spaces
Elhoussine Azroul, Abdelmoujib Benkirane, Mohammed Shimi, Mohammed Srati
Abstract
In this paper, we are concerned with some qualitative properties of the new fractional Musielak–Sobolev spaces WsLΦx,y such that the generalized Poincaré type inequality and some continuous and compact embedding results. Moreover, we prove that any function in WsLΦx,y(Ω) may be extended to a function in WsLΦx,y(RN), with Ω⊂RN is a bounded domain of class C0,1. In addition, we establish a result that relates to the complemented subspace in WsLΦx,yRN. As an application, using the mountain pass theorem and some variational methods, we investigate the existence of a nontrivial weak solution for a class of nonlocal fractional type problems with Dirichlet boundary data.
Topics & Concepts
MathematicsEmbeddingSobolev spaceBounded functionType (biology)Pure mathematicsExtension (predicate logic)Class (philosophy)Sobolev inequalitySmoothnessFunction (biology)Boundary (topology)Mathematical analysisBiologyProgramming languageArtificial intelligenceEcologyEvolutionary biologyComputer scienceNonlinear Partial Differential EquationsNonlinear Differential Equations AnalysisNumerical methods in engineering