Results 41 to 50 of about 5,037 (196)

Affine Hardy–Littlewood–Sobolev inequalities

Journal of the European Mathematical Society
Sharp affine Hardy–Littlewood–Sobolev inequalities for functions on \mathbb{R}^{n} are established, which are significantly stronger than (and directly imply) the sharp Hardy–Littlewood–Sobolev inequalities by Lieb and by Beckner, Dou, and Zhu.
Julián Eduardo Haddad, Monika Ludwig
openaire   +2 more sources

Ground state solutions for nonlinearly coupled systems of Choquard type with lower critical exponent

Electronic Journal of Qualitative Theory of Differential Equations, 2020
In this paper, we study the existence of ground state solutions for the following nonlinearly coupled systems of Choquard type with lower critical exponent by variational methods \begin{equation*} \begin{cases} \displaystyle-\Delta u+V(x)u=(I_\alpha\ast ...
Anran Li, Peiting Wang, Chongqing Wei
doaj   +1 more source

Symmetry and Nonexistence of Positive Solutions for Weighted HLS System of Integral Equations on a Half Space

Abstract and Applied Analysis, 2014
We consider system of integral equations related to the weighted Hardy-Littlewood-Sobolev (HLS) inequality in a half space. By the Pohozaev type identity in integral form, we present a Liouville type theorem when the system is in both supercritical and ...
Linfen Cao, Zhaohui Dai
doaj   +1 more source

Reverse Hardy-Littlewood-Sobolev inequalities

, 2018
This paper is devoted to a new family of reverse Hardy-Littlewood-Sobolev inequalities which involve a power law kernel with positive exponent. We investigate the range of the admissible parameters and characterize the optimal functions. A striking open question is the possibility of concentration which is analyzed and related with nonlinear diffusion ...
Dolbeault, Jean, Frank, Rupert, Hoffmann, Franca   +2 more
openaire   +2 more sources

On the stability of a version of nonlocal Sobolev inequality

Bulletin of Mathematical Sciences
In this paper, we investigate the stability of the corresponding nonlocal Sobolev inequality ∫ℝN|Δu|2dx≥S∗∫ℝN(|x|−α∗|u|p)updx1p,∀u∈𝒟2,2(ℝN), where [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] is the best constant.
Weiwei Ye, Xinyun Zhang
doaj   +1 more source

Solutions with prescribed mass for a critical Choquard equation driven by a local-nonlocal operator [PDF]

Opuscula Mathematica
In this paper, we study the normalized solutions of the following critical growth Choquard equation with mixed local and nonlocal operators: \[\begin{split}-\Delta u +(-\Delta)^s u &= \lambda u +\mu |u|^{p-2}u +(I_{\alpha}*|u|^{2^*_{\alpha}})|u|^{2^*_ ...
Nidhi Nidhi, Konijeti Sreenadh
doaj   +1 more source

A strong quantitative form of the fractional isoperimetric inequality

Journal of the London Mathematical Society, Volume 113, Issue 6, June 2026.
Abstract We show a strong version of the fractional quantitative isoperimetric inequality, in which the isoperimetric deficit controls not only the Fraenkel asymmetry but also a sort of oscillation of the boundary. This generalizes the local result by Fusco and Julin in [22].
Eleonora Cinti, Enzo Maria Merlino, Berardo Ruffini   +2 more
wiley   +1 more source

The HELP inequality on trees

, 2008
We establish analogues of Hardy and Littlewood's integro-differential equation for Schrödinger-type operators on metric and discrete trees, based on a generalised strong limit-point property of the graph ...
Matthias Langer, Karl Michael Schmidt, Langer, M., Brown, Brian Malcolm, Brown, B. Malcolm, B. Malcolm Brown, Langer, Matthias, Schmidt, Karl Michael   +7 more
core   +1 more source

Littlewood, Paley and almost‐orthogonality: a theory well ahead of its time

Journal of the London Mathematical Society, Volume 113, Issue 5, May 2026.
Abstract The classic paper by Littlewood and Paley [J. Lond. Math. Soc. (1), 6 (1931), 230–233] marked the birth of Littlewood–Paley theory. We discuss this paper and its impact from a historical perspective, include an outline of the results in the paper and their subsequent significance in relation to developments over the last century, and set them ...
Anthony Carbery
wiley   +1 more source

Logarithmic Hardy-Littlewood-Sobolev inequality on pseudo-Einstein 3-manifolds and the logarithmic Robin mass [PDF]

, 2023
Given a three-dimensional pseudo-Einstein CR manifold (M, T1,0M, θ),vwe study the existence of a contact structure conformal to θ for which the logarithmic Hardy-Littlewood-Sobolev (LHLS) inequality holds.
Ali Maalaoui, Maalaoui, Ali
core   +1 more source