Results 1 to 10 of about 641,065 (281)
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
Sara Stevano
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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 +6 more sources
Integral representations and Liouville theorems for solutions of periodic elliptic equations [PDF]
, 2000 The paper contains integral representations for certain classes of exponentially growing solutions of second order periodic elliptic equations. These representations are the analogs of those previously obtained by S. Agmon, S. Helgason, and other authors
Kuchment, Peter, Pinchover, Yehuda
core +5 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
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
A Contribution of Liouville-Type Theorems to the Geometry in the Large of Hadamard Manifolds
Mathematics, 2022 A complete, simply connected Riemannian manifold of nonpositive sectional curvature is called a Hadamard manifold. In this article, we prove Liouville-type theorems for isometric and harmonic self-diffeomorphisms of Hadamard manifolds, as well as ...
Josef Mikeš +2 more
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Optimal Liouville theorems for superlinear parabolic problems [PDF]
, 2020 Liouville theorems for scaling invariant nonlinear parabolic equations and systems (saying that the equation or system does not possess positive entire solutions) guarantee optimal universal estimates of solutions of related initial and initial-boundary ...
P. Quittner
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Partial regularity and Liouville theorems for stable solutions of anisotropic elliptic equations [PDF]
Discrete and Continuous Dynamical Systems. Series A, 2020 We study the quasilinear elliptic equation \begin{equation*} -Qu=e^u \ \ \text{in} \ \ \Omega\subset \mathbb{R}^{N} \end{equation*} where the operator $Q$, known as Finsler-Laplacian (or anisotropic Laplacian), is defined by $$Qu:=\sum_{i=1}^{N}\frac ...
Mostafa Fazly, Yuan Li
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Liouville Theorems for a Stationary and Non-stationary Coupled System of Liquid Crystal Flows in Local Morrey Spaces [PDF]
Journal of Mathematical Fluid Mechanics, 2020 We consider here the simplified Ericksen–Leslie system on the whole space R3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \
Oscar Jarŕın
semanticscholar +1 more source
AIMS Mathematics, 2022 In this study, we have presented two new alternative definitions corresponding to the basic definitions of the discrete delta and nabla fractional difference operators. These definitions and concepts help us in establishing a relationship between Riemann-
Juan L. G. Guirao +4 more
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