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The method of moving planes: a quantitative approach
Bruno Pini Mathematical Analysis Seminar, 2018 We review classical results where the method of the moving planes has been used to prove symmetry properties for overdetermined PDE's boundary value problems (such as Serrin's overdetermined problem) and for rigidity problems in geometric analysis (like ...
Giulio Ciraolo, Alberto Roncoroni
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Asymptotic method of moving planes for fractional parabolic equations [PDF]
Advances in Mathematics, 2020 In this paper, we develop a systematical approach in applying an asymptotic method of moving planes to investigate qualitative properties of positive solutions for fractional parabolic equations. We first obtain a series of needed key ingredients such as
Wenxiong Chen +3 more
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A direct method of moving planes for the fractional Laplacian [PDF]
Advances in Mathematics, 2014 In this paper, we develop a direct method of moving planes for the fractional Laplacian. Instead of conventional extension method introduced by Caffarelli and Silvestre, we work directly on the non-local operator.
Wenxiong Chen, Congming Li, Yan Li
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Some notes on the method of moving planes [PDF]
Bulletin of the Australian Mathematical Society, 1992 In this paper, we obtain a version of the sliding plane method of Gidas, Ni and Nirenberg which applies to domains with no smoothness condition on the boundary. The method obtains results on the symmetry of positive solutions of boundary value problems for nonlinear elliptic equations.
E. N. Dancer
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Harnack Type Inequality: the Method of Moving Planes [PDF]
Communications in Mathematical Physics, 1999 Let \((M,g)\) be a compact Riemann surface without boundary and let \(\Delta_{g}\) be the associated Laplace-Beltrami operator. The main purpose of the paper is to provide a careful analysis of blowup solutions \((\xi_{n})\) in \(C^{2}(M)\) to the problems \[ - \Delta_{g} \xi_{n} = \lambda_{n} (V_{n} e^{\xi_{n}} - W_{n}) \quad\text{on \(M\)} , \qquad ...
Yanyan Li
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A sharp quantitative version of Alexandrov's theorem via the method of moving planes [PDF]
Journal of the European Mathematical Society, 2015 We prove the following quantitative version of the celebrated Soap Bubble Theorem of Alexandrov. Let $S$ be a $C^2$ closed embedded hypersurface of $\mathbb{R}^{n+1}$, $n\geq1$, and denote by $osc(H)$ the oscillation of its mean curvature.
Giulio Ciraolo, Luigi Vezzoni
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Some remarks on the method of moving planes
Differential and Integral Equations, 1998 In 1979, Gidas, Ni, and Nirenberg [3.] est.ablish radial symmetry of positive solufions to certain nonlinear elliptic equations. The technique is based on the maximum principle.
L. Damascelli
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A direct method of moving planes for the fractional p-Laplacian system with negative powers
Indian Journal of Pure and Applied Mathematics, 2022 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Minghui Qie, Zhongxue Lü, Xin Zhang
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Estimates of the conformal scalar curvature equation via the method of moving planes [PDF]
Communications on Pure and Applied Mathematics, 1997 This paper is motivated by the problem of finding a metric conformal to the standard metric of \(\mathbb R^n\) with bounded prescribed scalar curvature \(K(x).\) For a survey of the first achievements on this problem, see the book of \textit{Th. Aubin} [Some Nonlinear Problems in Riemannian Geometry, Springer (1998; Zbl 0896.53003)].
Chiun-Chuan Chen, Changshou Lin
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Direct method of moving planes for logarithmic Laplacian system in bounded domains
Discrete & Continuous Dynamical Systems - A, 2018 Chen, Li and Li [Adv. Math., 308(2017), pp. 404-437] developed a direct method of moving planes for the fractional Laplacian. In this paper, we extend their method to the logarithmic Laplacian. We consider both the logarithmic equation and the system. To
Baiyu Liu
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