Publication | Open Access
Some remarks about the summability of nonlocal nonlinear problems
33
Citations
0
References
2015
Year
Spectral TheoryDirichlet FormElliptic EquationEngineeringNonlocal Nonlinear ProblemsVariational AnalysisPotential TheoryFinite Energy SolutionsFunctional AnalysisNonlocal OperatorsNonlocal PCalculus Of VariationVariational InequalitiesNonlinear Functional Analysis
Abstract In this note, we will study the problem (-Δ) p s u = f ( x ) on Ω, u = 0 in ℝ N ∖Ω, where 0 < s < 1, (-Δ) p s is the nonlocal p -Laplacian defined below, Ω is a smooth bounded domain. The main point studied in this work is to prove, adapting the techniques used in [`Basic estimates for solution of elliptic and parabolic equations for a class of nonlocal operators', Discrete Contin. Dyn. Syst., to appear] for the case p = 2 to the general case p ∈ (1, +∞), the summability of the finite energy solutions in terms of the summability of a source term f ( x ). The aim of this note is to present the results in a way as elementary as possible.