Results 91 to 100 of about 5,037 (196)
The sharp constant in the Hardy-Sobolev-Maz'ya inequality in the three dimensional upper half-space
, 2008 It is shown that the sharp constant in the Hardy-Sobolev-Maz'ya inequality on the upper half space H-3 subset of R-3 is given by the Sobolev constant.
Frank, Rupert L., +2 more
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Ground state solution for Schrödinger-Choquard equation: doubly critical case
Boundary Value ProblemsIn this paper, we investigate the following Schrödinger-Choquard equation: − Δ u + u = ( I α ∗ | u | 2 α ♯ ) | u | 2 α ♯ − 2 u + | u | q − 2 u + | u | r − 2 u , x ∈ R N , $$ -\Delta u+u = (I_{\alpha }*|u|^{2_{\alpha }^{\sharp }})|u|^{2_{\alpha }^{ \sharp
Yusheng Shen, Zhiwei Zou, You Gao
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The sharp constant in the Hardy-Sobolev-Maz’ya inequality in the three dimensional upper half-space [PDF]
, 2007 It is shown that the sharp constant in the Hardy-Sobolev-Maz’ya inequality on the upper half space H^3 ⊂ R^3 is given by the Sobolev constant. This is achieved by a duality argument relating the problem to a Hardy-Littlewood-Sobolev type inequality whose
Benguria, Rafael D. +2 more
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Regularity lifting result for an integral system involving Riesz potentials
Electronic Journal of Differential Equations, 2017 In this article, we study the integral system involving the Riesz potentials $$\displaylines{ u(x)=\sqrt{p} \int_{\mathbb{R}^n}\frac{u^{p-1}(y)v(y)dy}{|x-y|^{n-\alpha}}, \quad u>0 \text{ in } \mathbb{R}^n,\cr v(x)=\sqrt{p} \int_{\mathbb{R}^n}\frac{u ...
Yayun Li, Deyun Xu
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Existence of extremals for stability of nonlocal Sobolev inequality
Advanced Nonlinear StudiesThis paper is devoted to quantitative refinements of the nonlocal Sobolev inequality with explicit determination of stability constants. In the single-bubble regime, we rigorously prove that the optimal stability constantcHLS=infu∈D1,2(RN)\M‖∇u‖L2(RN)2 ...
Zhang Qian
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Hardy-Sobolev Inequalities [PDF]
, 2022 Στην παρούσα εργασία θα μελετηθούν δύο ανισότητες Hardy-Sobolev, μια που αφορά απόσταση από σημείο και μια που αφορά απόσταση από σύνορο. Για την ανισότητα Hardy-Sobolev που αφόρα απόσταση απο σημείο βρίσκουμε βέλτιστη σταθερά.
Akrivou Eleni-Ioanna +1 more
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Hardy-Littlewood-Sobolev inequality in total Morrey spaces
PositivityWe study some necessary and sufficient conditions for the boundedness of the Riesz potential operator Iα and its commutator on the total Morrey spaces Lp,λ,μ(Rn). We characterize the strong and weak Spanne type and Adams type boundedness of Iα on Lp,λ,μ(Rn), respectively.
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Hardy-Littlewood-Sobolev inequality on product spaces
, 2018 We study a family of fractional integral operator defined on an homogeneous space with a "rectangle doubling" measure. As a result, we give an extension of the classical Hardy-Littlewood-Sobolev theorem to a multi-parameter setting.
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Spherical reflection positivity and the Hardy-Littlewood-Sobolev inequality
, 2010 We introduce the concept of spherical (as distinguished from planar) reflection positivity and use it to obtain a new proof of the sharp constants in certain cases of the HLS and the logarithmic HLS inequality. Our proofs relies on an extension of a work by Li and Zhu which characterizes the minimizing functions of the type $(1+|x|^2)^{-p}$.
Frank, Rupert L., Lieb, Elliott H.
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Approximation theory for weighted Sobolev spaces on curves [PDF]
, 2001 17 pages, no figures.-- MSC2000 codes: 41A10, 46E35, 46G10.MR#: MR1882649 (2003c:42002)In this paper we present a definition of weighted Sobolev spaces on curves and find general conditions under which the spaces are complete.
Pestana Galván, Domingo +6 more
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