Results 231 to 240 of about 5,661 (277)

Liouville’s Theorem for the Drifting Laplacian

Bulletin of the Malaysian Mathematical Sciences Society, 2022
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Fan Chen, Qihua Ruan, Weihua Wang
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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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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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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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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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Liouville theorem for X-elliptic operators

Nonlinear Analysis: Theory, Methods & Applications, 2009
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KOGOJ, ALESSIA ELISABETTA, Lanconelli, Ermanno   +1 more
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On Liouville’s Theorem for Biharmonic Functions

SIAM Journal on Applied Mathematics, 1971
The following theorem, called Liouville's theorem, is well known. THEOREM 1. Any harmonic function bounded either above or below in all of n-space is constant. The reader is referred to the excellent book by Protter and Weinberger [1] for the proof of the above theorem.
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A Liouville Theorem for Harmonic Maps

American Journal of Mathematics, 1995
The main result of the author is a Liouville type theorem for harmonic maps with domain \(M\), a complete Riemannian manifold of nonnegative Ricci curvature, and range \(N\), a simply-connected complete Riemannian manifold with sectional curvature bounded above by \(-a^2\), \(a>0\).
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Liouville’s theorems for Lévy operators

Mathematische Annalen
45 pages; minor ...
Tomasz Grzywny, Mateusz Kwaśnicki
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