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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
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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
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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.
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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
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A view on Liouville theorems in PDEs
Analysis and Geometry in Metric SpacesOur review of Liouville theorems includes a special focus on nonlinear partial differential equations and inequalities.
Mitidieri Enzo
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Liouville theorems for elliptic systems and applications
Journal of Mathematical Analysis and Applications, 2014 We prove different Liouville theorems for several classes of quasilinear elliptic systems and ...
Lorenzo DʼAmbrosio, E. Mitidieri
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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
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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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