Results 11 to 20 of about 5,037 (196)
Sobolev and Hardy–Littlewood–Sobolev inequalities
Journal of Differential Equations, 2014 This paper is devoted to improvements of Sobolev and Onofri inequalities. The additional terms involve the dual counterparts, i.e. Hardy-Littlewood-Sobolev type inequalities. The Onofri inequality is achieved as a limit case of Sobolev type inequalities.
Jankowiak, Gaspard, Dolbeault, Jean
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Sobolev and Hardy-Littlewood-Sobolev inequalities: duality and fast diffusion [PDF]
Mathematical Research Letters, 2011 In the euclidean space of dimension d ≥ 3, Sobolev and Hardy-Littlewood-Sobolev inequalities can be related by duality. We investigate how to relate these inequalities using the flow of a fast diffusion equation. Up to a term which is needed for homogeneity reasons, the difference of the two terms in Sobolev's inequality can be seen as the derivative ...
Dolbeault, Jean
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Extremals in Hardy-Littlewood-Sobolev inequalities for stable processes
Journal of Mathematical Analysis and Applications, 2022 We prove the existence of an extremal function in the Hardy-Littlewood-Sobolev inequality for the energy associated to an stable operator. To this aim we obtain a concentration-compactness principle for stable processes in $\mathbb{R}^N$.
de Pablo, Arturo +2 more
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Choquard-type equations with Hardy–Littlewood–Sobolev upper-critical growth [PDF]
Advances in Nonlinear Analysis, 2018 We are concerned with the existence of ground states and qualitative properties of solutions for a class of nonlocal Schrödinger equations. We consider the case in which the nonlinearity exhibits critical growth in the sense of the Hardy–Littlewood ...
Cassani Daniele, Zhang Jianjun
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Fractional Sobolev and Hardy-Littlewood-Sobolev inequalities
, 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 a new, simpler proof and provide new estimates on the best constant involved.
Jankowiak, Gaspard, Nguyen, Van Hoang
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A New, Rearrangement-free Proof of the Sharp Hardy–Littlewood–Sobolev Inequality [PDF]
, 2011 We show that the sharp constant in the Hardy-Littlewood-Sobolev inequality can be derived using the method that we employed earlier for a similar inequality on the Heisenberg group. The merit of this proof is that it does not rely on rearrangement inequalities; it is the first one to do so for the whole parameter range.
Frank, Rupert L., Lieb, Elliott H.
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On the stability of critical points of the Hardy-Littlewood-Sobolev inequality
, 2023 This paper is concerned with the quantitative stability of critical points of the Hardy-Littlewood-Sobolev inequality. Namely, we give quantitative estimates for the Choquard equation: $$-Δu=(I_μ\ast|u|^{2_μ^*}) u^{2_μ^*-1}\ \ \text{in}\ \ \R^N,$$ where $u>0,\ N\geq 3,\ μ\in(0,N)$, $I_μ$ is the Riesz potential and $2_μ^* \coloneqq \frac{2N-μ}{N-2 ...
Liu, Kuan, Zhang, Qian, Zou, Wenming
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Demonstratio MathematicaIn this article, we deal with the following pp-fractional Schrödinger-Kirchhoff equations with electromagnetic fields and the Hardy-Littlewood-Sobolev nonlinearity: M([u]s,Ap)(−Δ)p,Asu+V(x)∣u∣p−2u=λ∫RN∣u∣pμ,s*∣x−y∣μdy∣u∣pμ,s*−2u+k∣u∣q−2u,x∈RN,M({\left[u]}
Zhao Min +2 more
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Anisotropic Choquard problems with Stein–Weiss potential: nonlinear patterns and stationary waves
Comptes Rendus. Mathématique, 2021 Weighted inequality theory for fractional integrals is a relatively less known branch of calculus that offers remarkable opportunities to simulate interdisciplinary processes.
Zhang, Youpei +2 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. In doing this we extend a characterization of the minimizing functions due to Li and Zhu.
Frank, Rupert L., Lieb, Elliott H.
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