Results 21 to 30 of about 648,405 (147)

Reversed Stein–Weiss Inequalities with Poisson-Type Kernel and Qualitative Analysis of Extremal Functions

Advanced Nonlinear Studies, 2021
Through conformal map, isoperimetric inequalities are equivalent to the Hardy–Littlewood–Sobolev (HLS) inequalities involved with the Poisson-type kernel on the upper half space.
Tao Chunxia
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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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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., Delgadino, Matías G., Dolbeault, Jean, Frank, Rupert L., Hoffmann, Franca   +4 more
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Sharp Hardy–Littlewood–Sobolev inequalities on quaternionic Heisenberg groups [PDF]

Nonlinear Analysis, 2016
26 ...
Christ, Michael, Liu, Heping, Zhang, An
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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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An extended discrete Hardy-Littlewood-Sobolev inequality

Discrete and Continuous Dynamical Systems, 2014
Hardy-Littlewood-Sobolev (HLS) Inequality fails in the "critical" case: μ=n. However, for discrete HLS, we can derive a finite form of HLS inequality with logarithm correction for a critical case: μ=n and p=q, by limiting the inequality on a finite domain.
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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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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Estimation of Sobolev embedding constant on a domain dividable into bounded convex domains

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, Kazuaki Tanaka, Kouta Sekine, Shin’ichi Oishi   +3 more
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Affine logarithmic Hardy-Littlewood-Sobolev inequalities

An affine logarithmic Hardy-Littlewood-Sobolev inequality for functions on Rn is established, that is the limiting case (α → n) of the recent affine Hardy-Littlewood-Sobolev inequalities by Ludwig and Haddad. The new inequality is significantly stronger
Cai, Xiaxing
core   +4 more sources