Results 251 to 260 of about 174,938,743 (287)

On the method of moving planes and the sliding method

Boletim da Sociedade Brasileira de Matem�tica, 1991
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Berestycki, H., Nirenberg, L.
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The Maximum Principle and the Moving Plane Method

Resonance, 2020
In this article we discuss the maximum principle and it’s application to the study of symmetry of solutions of nonlinear partial differential equations, which was one of the main research topics of Louis Nirenberg. The central question in symmetry that we discuss is the following if a domain Ω ⊂ ℝN and the given boundary data on ∂Ω have some symmetry ...
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The Method of Moving Planes for Integral Equation in an Extremal Case

Journal of Partial Differential Equations, 2016
In this paper, we study the symmetry results and monotonicity of solutions for an integral equation $$u(x)=-c_N∫_{\mathbb{R}^N}e^{u(y)}log|x-y|dy$$ in an external case.
Ying Wang, Jian Wang
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Application of the method of moving planes to conformally invariant equations

Mathematische Zeitschrift, 2004
A basic question in Riemannian geometry is to determine to what extent curvature assumptions on the Riemannian metric \(g\) impose restrictions on the topology of \((M^n,g)\). Such a question is mainly motivated by the Gauss-Bonnet theorem for two-dimensional compact manifolds: \[ 2\pi\chi(M^2)=\int_{M^2}K\,d\mu\tag{1} \] where \(d\mu\) is the area ...
Guan, Peng-Fei, Lin, Chang-Shou, Wang, Guo-Fang   +2 more
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Moving plane methods for systems on half spaces

Mathematische Annalen, 2008
The author proves interesting versions of the moving plane theorem for cooperative systems of the type \[ -\Delta u= f(u,v),\qquad -\Delta v= g(u,v) \] in the half space \(T=\{x\in \mathbb R^N:x_1>0\},\) such that \(u=v=0\) on \(\partial T\). It is assumed that \(f,g\in C^1\) and the system is cooperative, that is, \(\partial f/\partial v\geq0\) and \(\
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A direct method of moving planes for the system of the fractional Laplacian

Pacific Journal of Mathematics, 2017
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Cheng, Chunxia, Lü, Zhongxue, Lü, Yingshu   +2 more
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Method and system of measuring ultrasonic signals in the plane of a moving web

The Journal of the Acoustical Society of America, 1996
An improved system for measuring the velocity of ultrasonic signals within the plane of moving web-like materials, such as paper, paperboard and the like. In addition to velocity measurements of ultrasonic signals in the plane of the web in the machine direction, MD, and a cross direction, CD, generally perpendicular to the direction of the traveling ...
HALL MACLIN S, JACKSON THEODORE G, WINK WILMER A, KNERR CHRISTOPHER   +3 more
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Direct Method of Moving Planes for Tempered Fractional Laplacian Equations

Frontiers of Mathematics
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Wang, Lu, Liu, Baiyu
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On the method of moving planes and symmetry of solutions of semilinear elliptic equations

Nonlinear Analysis: Theory, Methods & Applications, 1997
The method of moving planes is a powerful technique to show the radial symmetry of solutions of the semilinear equation \[ \Delta u+f(|x|,u)=0\quad\text{in }\Omega\quad\text{and}\quad u=k\quad\text{on }\partial\Omega,\tag{P} \] where \(\Omega\) is a radially symmetric domain in \(\mathbb{R}^n\). Usually it is applied under the conditions that (a) \(u(x)
Chen, Chiun-Chuan, Lee, Ming Di
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Estimates of the scalar curvature equation via the method of moving planes III

Communications on Pure and Applied Mathematics, 2000
This note continues previous work of the author and \textit{C.-C. Chen} [Part I, cf. ibid. 50, 971--1017 (1997; Zbl 0958.35013), Part II, J. Differ. Geom. 49, 115--178 (1998; Zbl 0961.35047)]. It continues to study the local behaviour or a positive singular solution of \(u\) of the equation \[ \Delta u+ K(x)^{{n+2\over n-2}}\leq 0\quad\text{in }B_2 ...
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