Results 241 to 250 of about 641,065 (281)
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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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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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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.
Purusottam Rath, M. Ram Murty
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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.
Purusottam Rath, M. Ram Murty
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On Local Type I Singularities of the Navier–Stokes Equations and Liouville Theorems
Journal of Mathematical Fluid Mechanics, 2018We prove that suitable weak solutions of the Navier–Stokes equations exhibit Type I singularities if and only if there exists a non-trivial mild bounded ancient solution satisfying a Type I decay condition.
D. Albritton, T. Barker
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Liouville theorems for some nonlinear inequalities [PDF]
Proceedings of the Steklov Institute of Mathematics, 2008 We prove various Liouville theorems for integral and differential inequalities on the whole RN. .
CARISTI, GABRIELLA +2 more
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A Strong Version of Liouville's Theorem
The American Mathematical Monthly, 20081. 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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On the Generalized Liouville Theorem
2019In this paper a generalization of the classical Liouville theorem for the solutions of special type elliptic systems and some nonclassical interpretations of this theorem are obtained.
Tamaz Vekua +3 more
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Liouville theorems for scaling invariant superlinear parabolic problems with gradient structure
, 2014We provide a simple method for obtaining new Liouville theorems for scaling invariant superlinear parabolic problems with gradient structure. To illustrate the method we prove Liouville theorems (guaranteeing nonexistence of positive classical solutions)
P. Quittner
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The American Mathematical Monthly, 1986
(1986). A Note on Liouville's Theorem. The American Mathematical Monthly: Vol. 93, No. 3, pp. 200-201.
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(1986). A Note on Liouville's Theorem. The American Mathematical Monthly: Vol. 93, No. 3, pp. 200-201.
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An extension of liouville's theorem
1979I . 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.
Richard Zippel, Joel Moses
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Archive for Rational Mechanics and Analysis, 2013
We study qualitative properties of positive solutions of noncooperative, possibly nonvariational, elliptic systems. We obtain new classification and Liouville type theorems in the whole Euclidean space, as well as in half-spaces, and deduce a priori ...
Alexandre Montaru +2 more
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We study qualitative properties of positive solutions of noncooperative, possibly nonvariational, elliptic systems. We obtain new classification and Liouville type theorems in the whole Euclidean space, as well as in half-spaces, and deduce a priori ...
Alexandre Montaru +2 more
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