Results 1 to 10 of about 30,045 (146)
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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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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Liouville Type Theorems Involving the Fractional Laplacian on the Upper Half Euclidean Space
Fractal and Fractional, 2022 In this paper, we mainly establish Liouville-type theorems for the elliptic semi-linear equations involving the fractional Laplacian on the upper half of Euclidean space.
Tao Zhang
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Accuracy Verification of 3D Motion Analysis System Using Smart-phone Monocular Camera [PDF]
Cheyuk gwahag yeon-gu, 2021 PURPOSE This study aimed to verify the accuracy of three-dimensional (3D) motion data produced through artificial intelligence-based user motion recognition technology with images obtained using a smartphone monocular camera. This was done to explore the
Jonghyun Yang +2 more
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Liouville-Type Theorem for Nonlinear Elliptic Equations Involving Generalized Greiner Operator
Mathematics, 2022 In this paper, we study the Liouville-type behaviors of the generalized Greiner operators with nonlinear boundary value conditions. We use the technique based upon the method of moving planes.
Wei Shi
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Radial symmetry for a generalized nonlinear fractional p-Laplacian problem
Nonlinear Analysis, 2021 This paper first introduces a generalized fractional p-Laplacian operator (–Δ)sF;p. By using the direct method of moving planes, with the help of two lemmas, namely decay at infinity and narrow region principle involving the generalized fractional p ...
Wenwen Hou +3 more
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A direct method of moving planes for logarithmic Schrödinger operator
Zeitschrift für Analysis und ihre Anwendungen, 2023 In this paper, we study the radial symmetry and monotonicity of nonnegative solutions to nonlinear equations involving the logarithmic Schrödinger operator (\mathcal{I}-\Delta)^{\log} corresponding to the logarithmic symbol
Rong Zhang +2 more
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Radially Symmetric Solution for Fractional Laplacian Systems with Different Negative Powers
Fractal and Fractional, 2022 By developing the direct method of moving planes, we study the radial symmetry of nonnegative solutions for a fractional Laplacian system with different negative powers: (−Δ)α2u(x)+u−γ(x)+v−q(x)=0,x∈RN, (−Δ)β2v(x)+v−σ(x)+u−p(x)=0,x∈RN, u(x)≳|x|a,v(x)≳|x ...
Haiyong Xu +3 more
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Moving plane method for varifolds and applications
American Journal of Mathematics, 2023 abstract: In this paper, we introduce a version of the moving plane method that applies to potentially quite singular hypersurfaces, generalizing the classical moving plane method for smooth hypersurfaces. Loosely speaking, our version for varifolds shows that smoothness and symmetry at infinity (respectively at the boundary) can be promoted to ...
Haslhofer, Robert +2 more
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Asymptotic method of moving planes for fractional parabolic equations [PDF]
Advances in Mathematics, 2021 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 narrow region principles, and various asymptotic maximum and strong maximum principles for ...
Chen, Wenxiong +3 more
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