Results 21 to 30 of about 6,369 (172)
Reverse Hardy–Littlewood–Sobolev inequalities
Journal de Mathématiques Pures et Appliquées, 2019 This paper is based on the merging of arXiv:1803.06151 and arXiv:1803 ...
Carrillo, José A. +4 more
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Ground state sign-changing solutions for critical Choquard equations with steep well potential
Electronic Journal of Qualitative Theory of Differential Equations, 2022 In this paper, we study sign-changing solution of the Choquard type equation \begin{align*} -\Delta u+\left(\lambda V(x)+1\right)u =\big(I_\alpha\ast|u|^{2_\alpha^*}\big)|u|^{2_\alpha^*-2}u +\mu|u|^{p-2}u\quad \mbox{in}\ \mathbb{R}^N, \end{align*} where
Yong-Yong Li, Gui-Dong Li, Chun-Lei Tang
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The minimizing problem involving $p$-Laplacian and Hardy–Littlewood–Sobolev upper critical exponent
Electronic Journal of Qualitative Theory of Differential Equations, 2018 In this paper, we study the minimizing problem $$ S_{p,1,\alpha,\mu}:= \inf_{u\in W^{1,p}(\mathbb{R}^{N})\setminus\{0\}} \frac{ \int_{\mathbb{R}^{N}}|\nabla u|^{p}\mathrm{d}x - \mu \int_{\mathbb{R}^{N}} \frac{|u|^{p}}{|x|^{p}} \mathrm{d}x} {\left( \int_{\
Yu Su, Haibo Chen
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Hardy-Littlewood-Sobolev inequality for $p=1$
Sbornik: Mathematics, 2022 Let $\mathcal{W}$ be a closed dilation and translation invariant subspace of the space of $\mathbb{R}^\ell$-valued Schwartz distributions in $d$ variables. We show that if the space $\mathcal{W}$ does not contain distributions of the type $a\otimes \delta_0$, $\delta_0$ being the Dirac delta, then the inequality $\|\operatorname{I}_\alpha [f]\|_{L_{d ...
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Extremal problems of Hardy-Littlewood-Sobolev inequalities on compact Riemannian manifolds [PDF]
Journal of Mathematical Analysis and Applications, 2021 This paper studies the existence of extremal problems for the Hardy-Littlewood-Sobolev inequalities on compact manifolds without boundary via Concentration-Compactness principle.
Zhang, Shutao, Han, Yazhou
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An extended discrete Hardy-Littlewood-Sobolev inequality
Discrete & Continuous Dynamical Systems - A, 2014 Hardy-Littlewood-Sobolev (HLS) Inequality fails in the "critical" case: =n. However, for discrete HLS, we can derive a finite form of HLS inequality with logarithm correction for a critical case: =n and p=q, by limiting the inequality on a finite domain. The best constant in the inequality and its corresponding solution, the optimizer, are studied.
Cheng, Ze, Li, Congming
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Stability of Hardy Littlewood Sobolev inequality under bubbling
Calculus of Variations and Partial Differential Equations, 2023 AbstractIn this note we will generalize the results deduced in Figalli and Glaudo (Arch Ration Mech Anal 237(1):201–258, 2020) and Deng et al. (Sharp quantitative estimates of Struwe’s Decomposition. Preprint http://arxiv.org/abs/2103.15360, 2021) to fractional Sobolev spaces. In particular we will show that for $$s\in (0,1)$$
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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.
Frank, Rupert L., Lieb, Elliott H.
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Resistance Conditions and Applications
Analysis and Geometry in Metric Spaces, 2013 This paper studies analytic aspects of so-called resistance conditions on metric measure spaces with a doubling measure. These conditions are weaker than the usually assumed Poincaré inequality, but however, they are sufficiently strong to imply several ...
Kinnunen Juha, Silvestre Pilar
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Sharp Hardy–Littlewood–Sobolev inequalities on the octonionic Heisenberg group [PDF]
Calculus of Variations and Partial Differential Equations, 2016 The Hardy-Littlewood-Sobolev inequality for the conjugate exponent on a group of Heisenberg type has the form \[ \left|\iint_{G\times G}\frac{\overline{f(u)}g(v)}{|u^{-1}v|^\lambda}dudv\right|\lesssim\|f\|_p\|g\|_p, \] where ...
Christ, Michael, Liu, Heping, Zhang, An
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