Results 1 to 10 of about 654,091 (289)

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   +6 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   +6 more sources

Liouville theorems on the upper half space [PDF]

Discrete and Continuous Dynamical Systems. Series A, 2020
In this paper we shall establish some Liouville theorems for solutions bounded from below to certain linear elliptic equations on the upper half space.
Lei Wang, Mei‐Jun Zhu
openalex   +3 more sources

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

, 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   +4 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

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
core   +5 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

A new kind of uniqueness theorems for inverse Sturm-Liouville problems [PDF]

Boundary Value Problems, 2017
We prove Marchenko-type uniqueness theorems for inverse Sturm-Liouville problems. Moreover, we prove a generalization of Ambarzumyan’s theorem.
Yuri Ashrafyan
doaj   +2 more sources

Classification of supersolutions and Liouville theorems for some nonlinear elliptic problems

, 2016
In this paper we consider positive supersolutions of the elliptic equation $-\triangle u = f(u) |\nabla u|^q$, posed in exterior domains of $\mathbb{R}^N$ ($N\ge 2$), where $f$ is continuous in $[0,+\infty)$ and positive in $(0,+\infty)$ and $q>0$.
Alexander Quaas, Jorge García-Melián, M.Á. Burgos-Pérez   +2 more
openalex   +2 more sources

On some Liouville theorems for $ p $-Laplace type operators

Communications in Analysis and Mechanics
The aim of this note is to examine Liouville-type theorems for $ p $-Laplacian-type operators. Guided by the Laplacian case, analogous results are established for the $ p $-Laplacian and sums of operators of this type.
Michel Chipot, Daniel Hauer
doaj   +2 more sources