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Sharp Liouville Theorems [PDF]

Advanced Nonlinear Studies, 2021
Consider the equation div⁡(φ2⁢∇⁡σ)=0{\operatorname{div}(\varphi^{2}\nabla\sigma)=0} in ℝN{\mathbb{R}^{N}}, where φ>0{\varphi>0}. Berestycki, Caffarelli and Nirenberg proved in [H. Berestycki, L. Caffarelli and L. Nirenberg, Further qualitative properties
Villegas Salvador
doaj   +7 more sources

Liouville Theorems for Fractional Parabolic Equations [PDF]

Advanced Nonlinear Studies, 2021
In this paper, we establish several Liouville type theorems for entire solutions to fractional parabolic equations. We first obtain the key ingredients needed in the proof of Liouville theorems, such as narrow region principles and maximum principles for
Chen Wenxiong, Wu Leyun
doaj   +2 more sources

Nonlinear Dirac Equations, Monotonicity Formulas and Liouville Theorems. [PDF]

Commun Math Phys, 2019
We study the qualitative behavior of nonlinear Dirac equations arising in quantum field theory on complete Riemannian manifolds. In particular, we derive monotonicity formulas and Liouville theorems for solutions of these equations.
Branding V.
europepmc   +3 more sources

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 C 1 regularity of the foliation by invariant Lagrangian tori is crucial to prove the continuity of ...
Marie-Claude Arnaud, Jinxin Xue
openalex   +4 more sources

${L^p}$-Liouville Theorems for Invariant Partial Differential Operators in ${\mathbb{R}^n}$

, 2014
We prove some $L^p$-Liouville theorems for hypoelliptic second order Partial Differential Operators left translation invariant with respect to a Lie group composition law in $\mathbb{R}^n$.
Kogoj, Alessia E., Lanconelli, Ermanno
core   +3 more sources

On Cauchy–Liouville-type theorems

Advances in Nonlinear Analysis, 2017
In this paper we explore Liouville-type theorems to solutions of PDEs involving the ϕ-Laplace operator in the setting of Orlicz–Sobolev spaces. Our results extend Liouville-type theorems that have been obtained recently.
Araya Ataklti, Mohammed Ahmed
doaj   +2 more sources

Weak Liouville-Arnold Theorems & Their Implications [PDF]

Communications in Mathematical Physics, 2012
This paper studies the existence of invariant smooth Lagrangian graphs for Tonelli Hamiltonian systems with symmetries. In particular, we consider Tonelli Hamiltonians with n independent but not necessarily involutive constants of motion and obtain two ...
A. Fathi, A. Fathi, A. Sorrentino, Alfonso Sorrentino, D. Montgomery, H. Mineur, H.J. Sussmann, H.J. Sussmann, I. Agol, I.A. Taĭmanov, J. Hempel, J.J. Duistermaat, J.N. Mather, J.N. Mather, K. Dekimpe, L. Auslander, L. Bates, L.T. Butler, Leo T. Butler, M.C. Arnaud, M.J. Dias Carneiro, N.M. Dunfield, P. Bernard, P. Bernard, P. Stefan, R. Mañé, S. Schwartzman, V.V. Kozlov   +27 more
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A view on Liouville theorems in PDEs

Analysis and Geometry in Metric Spaces
Our review of Liouville theorems includes a special focus on nonlinear partial differential equations and inequalities.
Mitidieri Enzo
doaj   +3 more sources

Some Liouville theorems for stationary Navier-Stokes equations in Lebesgue and Morrey spaces [PDF]

Annales de l'Institut Henri Poincare. Analyse non linéar, 2018
Diego Chamorro, Oscar Jarrín, Pierre Gilles Lemarié–Rieusset   +2 more
openalex   +3 more sources

Universal estimates and Liouville theorems for superlinear problems without scale invariance [PDF]

Discrete and Continuous Dynamical Systems. Series A, 2022
We revisit rescaling methods for nonlinear elliptic and parabolic problems and show that, by suitable modifications, they may be used for nonlinearities that are not scale-invariant even asymptotically and whose behavior can be quite far from power like ...
P. Souplet
semanticscholar   +1 more source