Results 1 to 10 of about 30,449 (184)
, 2019 In this paper, we propose accurate and efficient finite difference methods to discretize the two- and three-dimensional fractional Laplacian $(-\Delta)^{\frac{\alpha}{2}}$ ($0 < \alpha < 2$) in hypersingular integral form.
Duo, Siwei, Zhang, Yanzhi
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Fractional p-Laplacian evolution equations
Journal de Mathématiques Pures et Appliquées, 2016 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Mazón, José M. +2 more
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Singular Continuous Spectrum for the Laplacian on Certain Sparse Trees
, 2006 We present examples of rooted tree graphs for which the Laplacian has singular continuous spectral measures. For some of these examples we further establish fractional Hausdorff dimensions.
B. Simon +12 more
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Variational Inequalities for the Fractional Laplacian [PDF]
Potential Analysis, 2016 19 ...
MUSINA, Roberta +2 more
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Non-Nehari Manifold Method for Fractional p-Laplacian Equation with a Sign-Changing Nonlinearity
Journal of Function Spaces, 2018 We consider the following fractional p-Laplacian equation: -Δpαu+V(x)up-2u=f(x,u)-Γ(x)uq-2u, x∈RN, where N≥2, pα⁎>q>p≥2, α∈(0,1), -Δpα is the fractional p-Laplacian, and Γ∈L∞(RN) and Γ(x)≥0 for a.e. x∈RN. f has the subcritical growth but higher than Γ(x)
Huxiao Luo, Shengjun Li, Wenfeng He
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Fractional Laplacian with Supercritical Killings
Communications in Mathematical PhysicsIn this paper, we study Feynman-Kac semigroups of symmetric $\alpha$-stable processes with supercritical killing potentials belonging to a large class of functions containing functions of the form $b|x|^{-\beta}$, where $b>0$ and $\beta>\alpha$. We obtain two-sided estimates on the densities $p(t, x, y)$ of these semigroups for all $t>0$, along with ...
Soobin Cho, Renming Song
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Hopf's lemmas for parabolic fractional Laplacians and parabolic fractional $p$-Laplacians
, 2020 In this paper, we first establish Hopf's lemmas for parabolic fractional equations and parabolic fractional $p$-equations. Then we derive an asymptotic Hopf's lemma for antisymmetric solutions to parabolic fractional equations. We believe that these Hopf's lemmas will become powerful tools in obtaining qualitative properties of solutions for nonlocal ...
Wang, Pengyan, Chen, Wenxiong
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The fractional Laplacian has infinite dimension [PDF]
Communications in Partial Differential Equations, 2019 We show that the fractional Laplacian on $\mathbb{R}^d$ fails to satisfy the Bakry- mery curvature-dimension inequality $CD( ,N)$ for all curvature bounds $ \in \mathbb{R}$ and all finite dimensions $N>0$.
Adrian Spener +2 more
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Fractional Laplacian in conformal geometry
Advances in Mathematics, 2011 In this note, we study the connection between the fractional Laplacian operator that appeared in the recent work of Caffarelli-Silvestre and a class of conformally covariant operators in conformal geometry.
González Nogueras, María del Mar +1 more
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Getting Acquainted with the Fractional Laplacian [PDF]
, 2019 updated version, 72 pages, 12 ...
Abatangelo N., Valdinoci E.
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