Robin fractional problems with symmetric variable growth
Anouar Bahrouni, Vicenţiu D. Rădulescu, Patrick Winkert
Abstract
In this paper, we study the fractional p(⋅, ⋅)-Laplacian, and we introduce the corresponding nonlocal conormal derivative for this operator. We prove the basic properties of the corresponding function space, and we establish a nonlocal version of the divergence theorem for such operators. In the second part of this paper, see Sec. IV, we prove the existence of weak solutions of corresponding p(⋅, ⋅)-Robin boundary problems with sign-changing potentials by applying variational tools.
Topics & Concepts
MathematicsBoundary value problemVariable (mathematics)Mathematical analysisDivergence (linguistics)Applied mathematicsFunction (biology)Boundary (topology)Pure mathematicsFractional calculusExistence theoremTime derivativeVariational principleSymmetric functionWeak solutionDerivative (finance)Penalty methodNonlinear Partial Differential EquationsNonlinear Differential Equations AnalysisNonlocal and gradient elasticity in micro/nano structures