Results 11 to 20 of about 39,002 (292)
A direct method of moving planes for a fully nonlinear nonlocal system
Communications on Pure & Applied Analysis, 2017 In this paper we consider the system involving fully nonlinear nonlocal operators: \begin{document}$ \left\{\begin{array}{ll}{\mathcal F}_{α}(u(x)) = C_{n,α} PV ∈t_{\mathbb{R}^n} \frac{F(u(x)-u(y))}{|x-y|^{n+α}} dy=v^p(x)+k_1(x)u^r(x),\\{\mathcal G}_{β ...
Pengyan Wang, P. Niu
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Journal of the European Mathematical Society, 2010 In this paper we deal with maximum principles for a class of linear, degenerate elliptic differential operators of the second order. In particular the Weak and Strong Maximum Principles are shown to hold for this class of operators in bounded domains, as well as a Hopf type lemma, under suitable hypothesis on the degeneracy set of ...
D. Monticelli
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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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Snapshot Quantitative Phase Imaging with Acousto-Optic Chromatic Aberration Control [PDF]
SensorsThe transport of intensity equation enables quantitative phase imaging from only two axially displaced intensity images, facilitating the characterization of low-contrast samples like cells and microorganisms.
Christos Alexandropoulos +2 more
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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 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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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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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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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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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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