An elliptic boundary value problem with fractional nonlinearity
Nicola Abatangelo, Matteo Cozzi
2021Archivio istituzionale della ricerca (Alma Mater Studiorum Università di Bologna)41 citationsDOIOpen Access PDF
Abstract
We investigate the existence and uniqueness of solutions to second-order elliptic boundary value problems containing a power nonlinearity applied to a fractional Laplacian. We detect the critical power separating the existence from the nonexistence regimes. For the existence results, we make use of a particular class of weighted Sobolev spaces to compensate for boundary singularities which are naturally built in the problem.
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MathematicsSobolev spaceUniquenessMathematical analysisBoundary value problemNonlinear systemGravitational singularityClass (philosophy)Fractional LaplacianLaplace operatorBoundary (topology)Order (exchange)PhysicsFinanceQuantum mechanicsArtificial intelligenceEconomicsComputer scienceNonlinear Partial Differential EquationsNonlinear Differential Equations AnalysisAdvanced Mathematical Physics Problems