2016 · 41 citations · 26 references
Natural SciencesMathematicsPhysicsDifferential EquationsMathematical PhysicsTheoretical PhysicsEigenvalue ProblemsHarmonic AnalysisNumerical AnalysisVariational FormulationVariational PrinciplesWeak FormulationEigenvalues Of The LaplacianFractional Differential EquationsLaplace Equation ExpansionsRegularity Criteria
Abstract. In this paper we establish a comparison result through symmetrization for so-lutions to some boundary value problems involving the fractional Laplacian. This allows to get sharp estimates for the solutions, obtained by comparing them with solutions of suitable radial problems. Furthermore, we use such result to prove a priori estimates for solutions in terms of the data, providing several regularity results which extend the well known ones for the classical Laplacian. 1. Introduction and
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