Results 1 to 10 of about 6,369 (172)
Hardy-Littlewood-Sobolev inequalities via fast diffusion flows. [PDF]
Proc Natl Acad Sci U S A, 2010 We give a simple proof of the λ = d - 2 cases of the sharp Hardy-Littlewood-Sobolev inequality for d ≥3, and the sharp Logarithmic Hardy-Littlewood-Sobolev inequality for d = 2 via a monotone flow governed by the fast diffusion equation.
Carlen EA, Carrillo JA, Loss M.
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Fractional Sobolev and Hardy-Littlewood-Sobolev inequalities [PDF]
Journal of Differential Equations, 2014 This work focuses on an improved fractional Sobolev inequality with a remainder term involving the Hardy-Littlewood-Sobolev inequality which has been proved recently. By extending a recent result on the standard Laplacian to the fractional case, we offer
Jankowiak, Gaspard, Nguyen, Van Hoang
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Hardy–Littlewood–Sobolev Inequality on Mixed-Norm Lebesgue Spaces [PDF]
The Journal of Geometric Analysis, 2022 We consider the Hardy-Littlewood-Sobolev inequality on mixed-norm Lebesgue spaces. We give a complete characterization of indices $\vec p$ and $\vec q$ such that the Riesz potential is bounded from $L^{\vec p}$ to $L^{\vec q}$, including all the endpoint cases. As a result, we get the mixed-norm Hardy-Littlewood-Sobolev inequality.
Ting Chen, Wenchang Sun
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Estimation of Sobolev embedding constant on a domain dividable into bounded convex domains [PDF]
Journal of Inequalities and Applications, 2017 This paper is concerned with an explicit value of the embedding constant from W 1 , q ( Ω ) $W^{1,q}(\Omega)$ to L p ( Ω ) $L^{p}(\Omega)$ for a domain Ω ⊂ R N $\Omega\subset\mathbb{R}^{N}$ ( N ∈ N $N\in\mathbb{N}$ ), where 1 ≤ q ≤ p ≤ ∞ $1\leq q\leq p ...
Makoto Mizuguchi +3 more
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Inversion positivity and the sharp Hardy-Littlewood-Sobolev inequality [PDF]
Calculus of Variations and Partial Differential Equations, 2009 We give a new proof of certain cases of the sharp HLS inequality. Instead of symmetric decreasing rearrangement it uses the reflection positivity of inversions in spheres.
Frank, Rupert L., Lieb, Elliott H.
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Hardy-Littlewood-Sobolev and Stein-Weiss inequalities on homogeneous Lie groups [PDF]
Integral Transforms and Special Functions, 2018 In this note we prove the Stein-Weiss inequality on general homogeneous Lie groups. The obtained results extend previously known inequalities. Special properties of homogeneous norms play a key role in our proofs.
Kassymov, Aidyn +2 more
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Sharp Hardy-Littlewood-Sobolev inequality on the upper half space [PDF]
International Mathematics Research Notices, 2013 There are at least two directions concerning the extension of classical sharp Hardy-Littlewood-Sobolev inequality: (1) Extending the sharp inequality on general manifolds; (2) Extending it for the negative exponent $\lambda=n-\alpha$ (that is for the ...
Dou, Jingbo, Zhu, Meijun
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Generalized Logarithmic Hardy–Littlewood–Sobolev Inequality [PDF]
International Mathematics Research Notices, 2020 Abstract This paper is devoted to logarithmic Hardy–Littlewood–Sobolev inequalities in the 2D Euclidean space, in the presence of an external potential with logarithmic growth. The coupling with the potential introduces a new parameter, with two regimes.
Dolbeault, Jean, Li, Xingyu
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Nonlinear Choquard equations on hyperbolic space [PDF]
Opuscula Mathematica, 2022 In this paper, our purpose is to prove the existence results for the following nonlinear Choquard equation \[-\Delta_{\mathbb{B}^{N}}u=\int_{\mathbb{B}^N}\dfrac{|u(y)|^{p}}{|2\sinh\frac{\rho(T_y(x))}{2}|^\mu} dV_y \cdot |u|^{p-2}u +\lambda u\] on the ...
Haiyang He
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Solutions for nonhomogeneous fractional (p, q)-Laplacian systems with critical nonlinearities
Advances in Nonlinear Analysis, 2022 In this article, we aimed to study a class of nonhomogeneous fractional (p, q)-Laplacian systems with critical nonlinearities as well as critical Hardy nonlinearities in RN{{\mathbb{R}}}^{N}.
Tao Mengfei, Zhang Binlin
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