Results 171 to 180 of about 695,650 (225)

A Liouville theorem for the Neumann problem of Monge-Ampère equations

Journal of Functional Analysis, 2022
In this paper, we study the Neumann problem of Monge-Ampère equations in Semi-space. For two dimensional case, we prove that its viscosity convex solutions must be a quadratic polynomial.
H. Jian, Xushan Tu
semanticscholar   +1 more source

Liouville’s Theorem for the Drifting Laplacian

Bulletin of the Malaysian Mathematical Sciences Society, 2022
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Fan Chen, Qihua Ruan, Weihua Wang
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Liouville Theorem for Heat Equation Along Ancient Super Ricci Flow Via Reduced Geometry

Journal of Geometric Analysis, 2020
The aim of this article is to provide a Liouville theorem for heat equation along ancient super Ricci flow. We formulate such a Liouville theorem under a growth condition concerning Perelman’s reduced distance.
Keita Kunikawa, Y. Sakurai
semanticscholar   +1 more source

THE LIOUVILLE THEOREM

1998
Abstract This result has a long history. For diffeomorphisms of class C in ℝ Liouville established the result in 1850 [204] along the lines we discussed in the chapter on conformal geometry. The relaxation of the differentiability hypotheses and the local injectivity assumptions are significant steps since the aim is to describe the ...
Tadeusz Iwaniec, Gaven Martin
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An extension of liouville's theorem

1979
I . Motivation, Computing integrals h0s been a favorite pastime of algebraic manipulators (bol, h human and machine) for some time. The usual problem is to determine if the integral of a function can be expressed in terms of some prespecitled set of functions.
Joel Moses, Richard Zippel
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Liouville theorem and classification of positive solutions for a fractional Choquard type equation

Nonlinear Analysis, 2019
Let n ≥ 2 , 0 α 2 and 0 β n . We prove that the equation ( − Δ ) α 2 u = 1 | x | n − β ∗ u p u p − 1 in R n has no positive solution if 1 ≤ p n + β n − α . We also classify all positive solutions to the equation in the critical case p = n + β n − α .
Phuong Le
semanticscholar   +1 more source

Liouville’s Theorem

2014
A complex number α is said to be an algebraic number if there is a non-zero polynomial \(f(x) \in \mathbb{Q}[x]\) such that f(α) = 0. Given an algebraic number α, there exists a unique irreducible monic polynomial \(P(x) \in \mathbb{Q}[x]\) such that P(α) = 0. This is called the minimal polynomial of α.
M. Ram Murty, Purusottam Rath
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A generalization of the Liouville–Arnol'd theorem

Mathematical Proceedings of the Cambridge Philosophical Society, 1995
AbstractWe show that the Liouville-Arnol'd theorem concerning knowledge of involutory first integrals for Hamiltonian systems is available for any system of second order ordinary differential equations. In establishing this result we also provide a new proof of the standard theorem in the setting of non-autonomous, regular Lagrangian mechanics on the ...
Prince, G. E., Byrnes, G. B., Sherring, J., Godfrey, S. E.   +3 more
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Liouville theorem for bounded harmonic functions on manifolds and graphs satisfying non-negative curvature dimension condition

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.
B. Hua
semanticscholar   +1 more source

A Strong Version of Liouville's Theorem

The American Mathematical Monthly, 2008
1. THE MAIN RESULT. Liouville's theorem states that every bounded holomor phic function on C is constant. Let us recall that holomorphic functions / on open subsets U of the complex plane have the mean value property, that is, for every closed disk B(z,r) in U, the value of / at its center z is equal to the average of the values of f on the circle S(z ...
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