The fractional Laplacian has infinite dimension
From MaRDI portal
Publication:5205886
DOI10.1080/03605302.2019.1663434zbMath1427.35338arXiv1903.00521OpenAlexW2974799445MaRDI QIDQ5205886
Adrian Spener, Frederic Weber, Rico Zacher
Publication date: 17 December 2019
Published in: Communications in Partial Differential Equations (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1903.00521
Fractional processes, including fractional Brownian motion (60G22) Smoothness and regularity of solutions to PDEs (35B65) Markov semigroups and applications to diffusion processes (47D07) Fractional partial differential equations (35R11)
Related Items (6)
Comparison principles for nonlocal Hamilton-Jacobi equations ⋮ The nonlocal inverse problem of Donsker and Varadhan ⋮ Li-Yau inequalities for general non-local diffusion equations via reduction to the heat kernel ⋮ Entropy solutions of doubly nonlinear fractional Laplace equations ⋮ Curvature-dimension inequalities for non-local operators in the discrete setting ⋮ The entropy method under curvature-dimension conditions in the spirit of Bakry-Émery in the discrete setting of Markov chains
Cites Work
- Unnamed Item
- Ten equivalent definitions of the fractional Laplace operator
- Nonlinear porous medium flow with fractional potential pressure
- A priori estimates for integro-differential operators with measurable kernels
- Drift diffusion equations with fractional diffusion and the quasi-geostrophic equation
- Fractional Laplacian phase transitions and boundary reactions: a geometric inequality and a symmetry result
- On the parabolic kernel of the Schrödinger operator
- Harnack inequalities for jump processes
- Curvature-dimension inequalities for non-local operators in the discrete setting
- The weak Harnack inequality for the Boltzmann equation without cut-off
- Nonlocal equations with measure data
- Quantitative local and global a priori estimates for fractional nonlinear diffusion equations
- Nonlinear equations for fractional Laplacians. I: Regularity, maximum principles, and Hamiltonian estimates
- Local Regularity for Parabolic Nonlocal Operators
- Regularity of the obstacle problem for a fractional power of the laplace operator
- Non-local Dirichlet forms and symmetric jump processes
- Regularity theory for fully nonlinear integro-differential equations
- Lévy Processes and Stochastic Calculus
- New Developments in the Analysis of Nonlocal Operators
- Analysis and Geometry of Markov Diffusion Operators
- An Extension Problem Related to the Fractional Laplacian
- Holder estimates for solutions of integro differential equations like the fractional laplace
- Nonlinear equations for fractional Laplacians II: Existence, uniqueness, and qualitative properties of solutions
- Geometric Analysis
- Optimal Transport
This page was built for publication: The fractional Laplacian has infinite dimension
