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A C^1 Arnol'd-Liouville theorem [PDF]
Astérisque, 2020 In this paper, we prove a version of Arnol'd-Liouville theorem for C 1 commuting Hamiltonians. We show that the Lipschitz regularity of the foliation by invariant Lagrangian tori is crucial to determine the Dynamics on each Lagrangian torus and that the ...
Marie-Claude Arnaud, Jinxin Xue
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Sharp Liouville Theorems [PDF]
Advanced Nonlinear Studies, 2020 Abstract Consider the equation div (
Salvador Villegas
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A Liouville theorem for Lévy generators [PDF]
Positivity, 2020 Under mild assumptions, we establish a Liouville theorem for the “Laplace” equation Au=0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs ...
F. Kühn
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Liouville theorem for bounded harmonic functions on manifolds and graphs satisfying non-negative curvature dimension condition [PDF]
Calculus of Variations and Partial Differential Equations, 2017 Brighton (in J Geom Anal 23(2):562–570, 2013) proved the Liouville theorem for bounded harmonic functions on weighted manifolds satisfying non-negative curvature dimension condition, i.e.
Bobo Hua
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On Liouville's theorem and the Strong Liouville Property [PDF]
In this paper we explore Liouville's theorem on Riemannian cones as defined below. We also study the Strong Liouville Property, that is, the property of a cone having spaces of harmonic functions of a fixed polynomial growth of finite dimension.
John E. Bravo, Jean C. Cortissoz
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A Liouville theorem for elliptic equations with a potential on infinite graphs [PDF]
Calculus of Variations and Partial Differential Equations, 2023 We investigate the validity of the Liouville property for a class of elliptic equations with a potential, posed on infinite graphs. Under suitable assumptions on the graph and on the potential, we prove that the unique bounded solution is u≡0 ...
Stefano Biagi, Giulia Meglioli, F. Punzo
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Quantum Liouville theorem based on Haar measure [PDF]
Physical review B, 2023 Liouville theorem (LT) reveals robust incompressibility of distribution function in phase space, given arbitrary potentials. However, its quantum generalization, Wigner flow, is compressible, i.e., LT is only conditionally true (e.g., for perfect ...
B. Q. Song +3 more
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Liouville theorem on Ricci shrinkers with constant scalar curvature and its application [PDF]
Journal für die Reine und Angewandte Mathematik, 2022 In this paper we consider harmonic functions on gradient shrinking Ricci solitons with constant scalar curvature. A Liouville theorem is proved without using gradient estimate: any bounded harmonic function is constant on gradient shrinking Ricci ...
Weixiong Mai, Jianyu Ou
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The Borg’s Theorem for Singular Sturm-Liouville Problem with Non-Separated Boundary Conditions [PDF]
Mathematics Interdisciplinary Research, 2023 In this paper, we consider a Sturm-Liouville equation with non-separated boundary conditions on a finite interval. We discuss some properties of solutions of the Sturm-Liouville equation, where the potential function has a singularity in the ...
Maedeh Bagherzadeh, Abdolali Neamaty
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AIMS Mathematics, 2023 The main purpose of this manuscript is to investigate the Sturm-Liouville BVP for non-autonomous Lagrangian systems. Under the suitable assumptions, we establish an existence theorem for three nonnegative solutions via Bonanno-Candito's three critical ...
Zhongqian Wang +2 more
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