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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A sharp quantitative version of Alexandrov's theorem via the method of moving planes [PDF]
Journal of the European Mathematical Society, 2018 We prove the following quantitative version of the celebrated Soap Bubble Theorem of Alexandrov. Let S be a C^2 closed ...
Giulio Ciraolo, Luigi Vezzoni
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Symmetry of Ground States of p -Laplace Equations via the Moving Plane Method [PDF]
Archive for Rational Mechanics and Analysis, 1999 The symmetry properties of positive solutions of the \(p\)-Laplace equation in \({\mathbb{R}}^N\), \(N\geq 2\) are studied with the ground state condition at infinity. By means of a weak comparison principle the main result is proved that a given solution is radially symmetric around some point \(x_0\in {\mathbb{R}}^N\).
DAMASCELLI L +2 more
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The method of moving planes for nonlocal uniformly fractional parabolic equations in a half space
Advances in Nonlinear AnalysisIn this paper, we consider the uniformly fractional parabolic equations in a half space∂u∂t(x,t)+Dasu(x,t)=f(u(x,t)),(x,t)∈R+n×R, $$\frac{\partial u}{\partial t}\left(x,t\right)+{\mathcal{D}}_{a}^{s}u\left(x,t\right)=f\left(u\left(x,t\right)\right ...
Tang Yanjuan
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Simulation of incompressible viscous flows around moving objects by a variant of immersed boundary-Lattice Boltzmann method [PDF]
, 2010 A variant of immersed boundary-lattice Boltzmann method (IB-LBM) is presented in this paper to simulate incompressible viscous flows around moving objects.
Zhang, Y.H., Wu, J., Shu, C.
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Implicitizing rational curves by the method of moving quadrics [PDF]
, 2019 International audienceA new technique for finding implicit matrix-based representations of rational curves in arbitrary dimension is introduced. It relies on the use of moving quadrics following curve parameterizations, providing a high-order extension ...
Busé, Laurent +2 more
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Maximum principles and the method of moving planes for the uniformly elliptic nonlocal Bellman operator and applications [PDF]
, 2022 In this paper, we establish various maximum principles and develop the method of moving planes and the sliding method (on general unbounded domains) for equations involving the uniformly elliptic nonlocal Bellman operator.
Qin, Guolin, Dai, Wei
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Analysis of a Hybrid Guided Bomb Control System while Self-guided to a Ground Target [PDF]
Problemy Mechatroniki, 2022 This article presents a mathematical model and an algorithm for controlling a guided bomb to a moving and a stationary ground target. The target path was determined from the kinematic relationships of the reciprocal movement of the bomb and the ground ...
Marta GRZYB, Zbigniew KORUBA
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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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