The Liouville theorem and linear operators satisfying the maximum principle

DOI10.1016/j.matpur.2020.08.008zbMath1448.35061arXiv1907.02495OpenAlexW3081303129MaRDI QIDQ2201786

Nathaël Alibaud, Jørgen Endal, Espen R. Jakobsen, Félix del Teso

Publication date: 17 September 2020

Published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1907.02495

zbMATH Keywords

Kronecker theoremLévy-Khintchine formulacourrège theoremnonlocal degenerate elliptic operatorspropagation of maximumsubgroups of \(\mathbb{R}^d\)

Mathematics Subject Classification ID

Processes with independent increments; Lévy processes (60G51) Numerical methods for integral equations (65R20) Periodic solutions to PDEs (35B10) Maximum principles in context of PDEs (35B50) Nonlinear elliptic equations (35J60) Degenerate elliptic equations (35J70) Integro-partial differential equations (35R09) Liouville theorems and Phragmén-Lindelöf theorems in context of PDEs (35B53)

Related Items (7)

On the Liouville property for fully nonlinear equations with superlinear first-order terms ⋮ Non-symmetric stable operators: regularity theory and integration by parts ⋮ Mixed local and nonlocal elliptic operators: regularity and maximum principles ⋮ Linear theory for a mixed operator with Neumann conditions ⋮ (Non)local logistic equations with Neumann conditions ⋮ Unnamed Item ⋮ A Liouville theorem for Lévy generators

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Kronecker's approximation theorem
• Liouville theorems for a general class of nonlocal operators
• Boundary regularity for fully nonlinear integro-differential equations
• Uniqueness and properties of distributional solutions of nonlocal equations of porous medium type
• On the coupling property and the Liouville theorem for Ornstein-Uhlenbeck processes
• Liouville theorems for non-local operators
• Liouville-type results for semilinear elliptic equations in unbounded domains
• Liouville type results for periodic and almost periodic linear operators
• On distributional solutions of local and nonlocal problems of porous medium type
• Gradient estimates for harmonic and \(q\)-harmonic functions of symmetric stable processes.
• On the strong maximum principle for second order nonlinear parabolic integro-differential equations
• Liouville's theorem and heat kernels
• Some Liouville theorems for the fractional Laplacian
• Nonlinear equations for fractional Laplacians. I: Regularity, maximum principles, and Hamiltonian estimates
• Entire $s$-harmonic functions are affine
• Phase Transitions with Midrange Interactions: A Nonlocal Stefan Model
• Robust Numerical Methods for Nonlocal (and Local) Equations of Porous Medium Type. Part II: Schemes and Experiments
• Financial Modelling with Jump Processes
• Liouville type results for a nonlocal obstacle problem
• Mathematical Pearls: A Proof of Liouville's Theorem

This page was built for publication: The Liouville theorem and linear operators satisfying the maximum principle