Integral representation for fractional Laplace–Beltrami operators
Copyright policy )Integral representation for fractional Laplace–Beltrami operators
In this paper we provide an integral representation of the fractional Laplace-Beltrami operator for general riemannian manifolds which has several interesting applications. We give two different proofs, in two different scenarios, of essentially the same result. One of them deals with compact manifolds with or without boundary, while the other approach treats the case of riemannian manifolds without boundary whose Ricci curvature is uniformly bounded below.
Hadamard's parametrix, Mathematics - Differential Geometry, Methods of local Riemannian geometry, fractional Laplace-Beltrami operator, Matemáticas, Fractional partial differential equations, Heat kernel on manifolds, Mathematics - Analysis of PDEs, Bochner subordination principle, Differential Geometry (math.DG), Fractional derivatives and integrals, Mathematics - Classical Analysis and ODEs, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Fractional Laplace–Beltrami operator, heat kernel on manifolds, Analysis of PDEs (math.AP)
Hadamard's parametrix, Mathematics - Differential Geometry, Methods of local Riemannian geometry, fractional Laplace-Beltrami operator, Matemáticas, Fractional partial differential equations, Heat kernel on manifolds, Mathematics - Analysis of PDEs, Bochner subordination principle, Differential Geometry (math.DG), Fractional derivatives and integrals, Mathematics - Classical Analysis and ODEs, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Fractional Laplace–Beltrami operator, heat kernel on manifolds, Analysis of PDEs (math.AP)
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