Some constructions for the fractional Laplacian on noncompact manifolds

DOI10.4171/RMI/850zbMath1334.58014arXiv1212.3109MaRDI QIDQ748341

María del Mar González, Mariel Sáez, Valeria Banica

Publication date: 20 October 2015

Published in: Revista Matemática Iberoamericana (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1212.3109

zbMATH Keywords

hyperbolic spaceextension problemnon-compact manifoldsfractional Laplaciansingular kernelFourier symbol

Mathematics Subject Classification ID

Degenerate elliptic equations (35J70) Pseudodifferential and Fourier integral operators on manifolds (58J40) Fractional partial differential equations (35R11) PDEs on manifolds (35R01)

Related Items

Well-posedness of a fractional porous medium equation on an evolving surface ⋮ Functional inequalities involving nonlocal operators on complete Riemannian manifolds and their applications to the fractional porous medium equation ⋮ Fourier analysis and optimal Hardy-Adams inequalities on hyperbolic spaces of any even dimension ⋮ Trace Hardy-Sobolev-Maz'ya inequalities on half space and sharp constant in dimension two ⋮ Extension problem and fractional operators: semigroups and wave equations ⋮ Sharp Hardy-Adams inequalities for bi-Laplacian on hyperbolic space of dimension four ⋮ Saddle-shaped solutions for the fractional Allen-Cahn equation ⋮ The fractional porous medium equation on manifolds with conical singularities II ⋮ Pointwise monotonicity of heat kernels ⋮ The fractional porous medium equation on the hyperbolic space ⋮ Li-Yau inequalities for general non-local diffusion equations via reduction to the heat kernel ⋮ Superdiffusive fractional in time Schrödinger equations: a unifying approach to superdiffusive waves ⋮ A nonlocal diffusion problem on manifolds ⋮ Layer solutions for the fractional Laplacian on hyperbolic space: existence, uniqueness and qualitative properties ⋮ Three representations of the fractional \(p\)-Laplacian: semigroup, extension and Balakrishnan formulas ⋮ Adams inequalities for Riesz subcritical potentials ⋮ On the infimum of the spectrum of a relativistic Schrödinger operator ⋮ On a fractional Ginzburg-Landau equation and 1/2-harmonic maps into spheres ⋮ Fractional diffusion maps ⋮ Sharp Adams and Hardy-Adams inequalities of any fractional order on hyperbolic spaces of all dimensions ⋮ Uniqueness of Radial Solutions for the Fractional Laplacian ⋮ Solutions of the fractional Allen–Cahn equation which are invariant under screw motion ⋮ Harnack inequality for nonlocal operators on manifolds with nonnegative curvature ⋮ On extension problem, trace Hardy and Hardy's inequalities for some fractional Laplacians ⋮ Fractional thoughts ⋮ An extension problem and Hardy's inequality for the fractional Laplace-Beltrami operator on Riemannian symmetric spaces of noncompact type ⋮ Symmetry and symmetry breaking for the fractional Caffarelli-Kohn-Nirenberg inequality

Cites Work

• Layer solutions for the fractional Laplacian on hyperbolic space: existence, uniqueness and qualitative properties
• Function theory on manifolds which possess a pole
• Fractional Laplacian in conformal geometry
• Singular solutions of fractional order conformal Laplacians
• Heat kernel bounds on manifolds with cusps
• \(\mathbb{L}_ p\) Fourier multipliers on Riemannian symmetric spaces of the noncompact type
• Harmonic analysis on solvable extensions of H-type groups
• Subelliptic estimates and function spaces on nilpotent Lie groups
• Théoremes de comparaison en géométrie Riemannienne
• Scattering matrix in conformal geometry
• Gaussian upper bounds for the heat kernels of some second-order operators on Riemannian manifolds
• Inversion formulas for the \(k\)-dimensional Radon transform in real hyperbolic spaces
• Best constants for Sobolev inequalities for higher order fractional derivatives
• Heat kernel and Green function estimates on noncompact symmetric spaces
• Geometrical finiteness for hyperbolic groups
• Hardy-Sobolev extremals, hyperbolic symmetry and scalar curvature equations
• Fractional conformal Laplacians and fractional Yamabe problems
• Weighted Strichartz estimates for radial Schrödinger equation on noncompact manifolds
• Heat Kernels of Metric Trees and Applications
• Schrödinger Equations on Damek–Ricci Spaces
• Heat Kernel Bounds on Hyperbolic Space and Kleinian Groups
• A lower bound for the heat kernel
• On the Upper Estimate of the Heat Kernel of a Complete Riemannian Manifold
• The local regularity of solutions of degenerate elliptic equations
• Stationary Gaussian random fields on hyperbolic spaces and on Euclidean spheres
• An Extension Problem Related to the Fractional Laplacian
• The Nonlinear Schrödinger Equation on Hyperbolic Space
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item