The Liouville theorem and linear operators satisfying the maximum principleA result by Courrège says that linear translation invariant operators satisfy the maximum principle if and only if they are of the form L=Lσ,b+Lμ whereLσ,b[u](x)=tr(σσTD2u(x))+bDu(x) andLμ[u](x)=∫...
The Liouville theorem for $$p$$p -harmonic functions and quasiminimizers with finite energyWe show that, under certain geometric conditions, there are no nonconstant quasiminimizers with finite pth power energy in a (not necessarily complete) metric measure space equipped with a globally doubling...
Liouville's theorem [′lyü‚vēlz ‚thir·əm] (mathematics) Every function of a complex variable which is bounded and analytic in the entire complex plane must be constant. McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc...
For the stationary weak solutions of the Euler-Poincaré equations we prove a Liouville type theorem. Namely, for α > 0 any weak solution u H1(mathbbRN){mathbf{u} in H^1(mathbb{R}^N)} is u=0; for α= 0 any weak solution u L2(mathbbRN){mathbf{u} in L^2(mathbb{R}^N)}...
A Liouville-type theorem for Lane-Emden system We provide a partial positive answer to a well-known conjecture about the nonexistence of positive solutions to Lane-Emden systems below the critical Sobol... J Busca,R Manasevich - 《Indiana University Mathematics Journal》 被引量: 160发表: 2002年...
Liouville's Theorem It is impossible to approximate rationally to an algebraic number of degree n with an order of accuracy higher than q^{-n}. Proof. Suppose \xi is an algebraic number of degree n defined by f(\xi)=a_0\xi^n+a_1\xi^{n-1}+\cdot\cdot\cdot+a_n=0. Suppose no...
We present a very short proof of Liouville's theorem for solutions to a nonuniformly elliptic radially symmetric equation. The proof uses the Ricatti equation satised by the Dirichlet to Neumann map. 关键词: Liouville's Theorem in the Radially Symmetric Case, Artículo DOI: 10.4153/CMB-2005-...
We are concerned with the Liouville property, i.e. the nonexistence of positive solutions in the whole space \({{\mathbb R}^N}\). We prove the optimal Liouville-type theorem for dimension N < m + 1 and give partial results for higher dimensions.关键词:...
Some Liouville theorems for the fractional Laplacian 来自 国家科技图书文献中心 喜欢 0 阅读量: 24 作者:Yan,Chen,Wenxiong,D'Ambrosio,Lorenzo 摘要: In this paper, we prove the following result. Let 关键词: The fractional Laplacian alpha-harmonic functions Liouville theorem Poisson representations ...
We prove a Liouville-type theorem for stable solution of the singular quasilinear elliptic equations div(|x|ap|u|p2u) = f(x)|u|q1u, in R , div(|x|ap|u|p2... C Chen,H Song,H Yang,... 被引量: 0发表: 2018年 Liouville type theorems for elliptic equations involving grushin oper...