Certain Liouville properties of eigenfunctions of elliptic operators

DOI10.1090/tran/7694zbMath1421.35072arXiv1708.09640OpenAlexW3098155967WikidataQ129216118 ScholiaQ129216118MaRDI QIDQ3120531

Anup Biswas, Debdip Ganguly, Aristotle Arapostathis

Publication date: 5 March 2019

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1708.09640

zbMATH Keywords

principal eigenvalueLiouville propertyLandis conjecture

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Second-order elliptic equations (35J15) Continuation and prolongation of solutions to PDEs (35B60) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Related Items (9)

On the monotonicity property of the generalized eigenvalue for weakly-coupled cooperative elliptic systems ⋮ An optimal improvement for the Hardy inequality on the hyperbolic space and related manifolds ⋮ On Landis' conjecture in the plane for some equations with sign-changing potentials ⋮ The Vázquez maximum principle and the Landis conjecture for elliptic PDE with unbounded coefficients ⋮ Exponential bounds for gradient of solutions to linear elliptic and parabolic equations ⋮ The Landis conjecture with sharp rate of decay ⋮ Generalized principal eigenvalues of convex nonlinear elliptic operators in \(\mathbb{R}^N\) ⋮ A Variational Characterization of the Risk-Sensitive Average Reward for Controlled Diffusions on $\mathbb{R}^d$ ⋮ Generalized principal eigenvalues on \({\mathbb{R}}^d\) of second order elliptic operators with rough nonlocal kernels

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Liouville properties and critical value of fully nonlinear elliptic operators
• On criticality and ground states of second order elliptic equations. II
• Criticality and ground states for second-order elliptic equations
• Structure of positive solutions to \((-\Delta +V)u=0\) in \(R^ n\)
• Pointwise bounds on eigenfunctions and wave packets in N-body quantum systems. V: Lower bounds and path integrals
• Large time behavior of the \(L^ p\) norm of Schrödinger semigroups
• Pointwise bounds for Schrödinger eigenstates
• On a conjecture of De Giorgi and some related problems
• The Radon transform.
• On variational principles for the generalized principal eigenvalue of second order elliptic operators and some applications
• Semismall perturbations in the Martin theory for elliptic equations
• First eigenvalues and comparison of Green's functions for elliptic operators on manifolds or domains
• On Green functions of second-order elliptic operators on Riemannian manifolds: the critical case
• Infinite horizon risk-sensitive control of diffusions without any blanket stability assumptions
• On positive solutions of second-order elliptic equations, stability results, and classification
• Existence of strong solutions for Itô's stochastic equations via approximations
• Optimal Hardy weight for second-order elliptic operator: an answer to a problem of Agmon
• On the possible decay at infinity of solutions of homogeneous elliptic equations
• The generalized principal eigenvalue for Hamilton-Jacobi-Bellman equations of ergodic type
• A Liouville-type theorem for Schrödinger operators
• A Liouville-type theorem for the \(p\)-Laplacian with potential term
• ON REGULARITY OF TRANSITION PROBABILITIES AND INVARIANT MEASURES OF SINGULAR DIFFUSIONS UNDER MINIMAL CONDITIONS
• Schrödinger semigroups
• Ergodic Control of Diffusion Processes
• Uniqueness theorems for second order elliptic differential equations
• ON QUALITATIVE PROPERTIES OF SOLUTIONS OF A NONLINEAR EQUATION OF SECOND ORDER
• On the Liouville Property for Divergence Form Operators
• Harnack's inequality for cooperative weakly coupled elliptic systems
• The principal eigenvalue and maximum principle for second‐order elliptic operators in general domains
• Generalizations and Properties of the Principal Eigenvalue of Elliptic Operators in Unbounded Domains
• On Landis’ Conjecture in the Plane
• The Landis conjecture for variable coefficient second-order elliptic PDEs
• Bounds for the Discrete Part of the Spectrum of a Semi-Bounded Schrödinger Operator.

This page was built for publication: Certain Liouville properties of eigenfunctions of elliptic operators