A direct method of moving planes for the fractional Laplacian
Advances in Mathematics, 2017 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. Using the integral defining the fractional Laplacian, by an elementary approach, we first obtain the key ingredients needed in the method of
Chen, Wenxiong, Li, Congming, Li, Yan
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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)].
Chen, Chiun-Chuan, Lin, Chang-Shou
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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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A direct method of moving planes for a fully nonlinear nonlocal system
Communications on Pure & Applied Analysis, 2017 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Wang, Pengyan, Niu, Pengcheng
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Direct method of moving planes for logarithmic Laplacian system in bounded domains
Discrete & Continuous Dynamical Systems - A, 2018 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Moving planes and sliding methods for fractional elliptic and parabolic equations
Advanced Nonlinear StudiesIn this paper, we summarize some of the recent developments in the area of fractional elliptic and parabolic equations with focus on how to apply the sliding method and the method of moving planes to obtain qualitative properties of solutions.
Chen Wenxiong, Hu Yeyao, Ma Lingwei
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Properties of solutions to fractional p-subLaplace equations on the Heisenberg group
Boundary Value Problems, 2020 The aim of this paper is to study properties of solutions to the fractional p-subLaplace equations on the Heisenberg group. Based on the maximum principles and the generalization of the direct method of moving planes, we obtain the symmetry and ...
Xinjing Wang, Guangwei Du
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Monotonicity and Symmetry of Solutions to Fractional Laplacian in Strips
Journal of Function Spaces, 2021 In this paper, using the method of moving planes, we study the monotonicity in some directions and symmetry of the Dirichlet problem involving the fractional Laplacian −Δα/2ux=fux,x∈Ω,ux>0,x∈Ω,ux=0,x∈ℝn\Ω, in a slab-like domain Ω=ℝn−1×0,h⊂ℝn.
Tao Sun, Hua Su
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Symmetry of standing waves for two kinds of fractional Hardy-Schrödinger equations
Alexandria Engineering Journal, 2021 In this paper, we consider two kinds of nonlinear Schrödinger equations with the fractional Laplacian and Hardy potential (λ|x|s ...
Guotao Wang +3 more
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Research on moving trajectory of intelligent sensor in underground roadway
Gong-kuang zidonghua, 2022 In order to solve the problem that the existing integrated inertial navigation method loses completely autonomous advantage and increases cost when applied to intelligent sensors in underground roadway, the underground roadways are firstly decomposed ...
BAI Sizhong
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