Results 91 to 100 of about 6,369 (172)

Limit case of Hardy-Littlewood-Sobolev inequality for martingales

, 2022
11 ...
openaire   +2 more sources

Boundary Strichartz estimates and pointwise convergence for orthonormal systems

Transactions of the London Mathematical Society, Volume 11, Issue 1, December 2024.
Abstract We consider maximal estimates associated with fermionic systems. Firstly, we establish maximal estimates with respect to the spatial variable. These estimates are certain boundary cases of the many‐body Strichartz estimates pioneered by Frank, Lewin, Lieb and Seiringer.
Neal Bez, Shinya Kinoshita, Shobu Shiraki   +2 more
wiley   +1 more source

Existence, symmetry, and regularity of ground states of a nonlinear Choquard equation in the hyperbolic space

Advances in Nonlinear Analysis
In this study, we explore the positive solutions of a nonlinear Choquard equation involving the Green kernel of the fractional operator (−ΔBN)−α⁄2{\left(-{\Delta }_{{{\mathbb{B}}}^{N}})}^{-\alpha /2} in the hyperbolic space, where ΔBN{\Delta }_{{{\mathbb{
Gupta Diksha, Sreenadh Konijeti
doaj   +1 more source

Nonexistence and existence of solutions for a Choquard–Kirchhoff type equation involving mixed local and nonlocal operators

Electronic Journal of Qualitative Theory of Differential Equations
In this paper, we study the following Choquard-Kirchhoff type equation $$ \left( a+b\|u\|^{p(\theta-1)}\right) \left( -\Delta_{p}u+(-\Delta)^{s}_{p}u\right) =\left( \int_{\mathbb R^N}\frac{|u(y)|^{p_{\mu}^{*}}}{|x-y|^\mu}dy\right) |u|^{p_{\mu}^{*}-2}u+\
Wenjing Chen, Jingran Feng
doaj   +1 more source

Conformally invariant random fields, Liouville quantum gravity measures, and random Paneitz operators on Riemannian manifolds of even dimension

Journal of the London Mathematical Society, Volume 110, Issue 5, November 2024.
Abstract For large classes of even‐dimensional Riemannian manifolds (M,g)$(M,g)$, we construct and analyze conformally invariant random fields. These centered Gaussian fields h=hg$h=h_g$, called co‐polyharmonic Gaussian fields, are characterized by their covariance kernels k which exhibit a precise logarithmic divergence: |k(x,y)−log1d(x,y)|≤C$\big ...
Lorenzo Dello Schiavo, Ronan Herry, Eva Kopfer, Karl‐Theodor Sturm   +3 more
wiley   +1 more source

Ground state solution for Schrödinger-Choquard equation: doubly critical case

Boundary Value Problems
In 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
doaj   +1 more source

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.
openaire   +3 more sources

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
doaj  

Existence of extremals for stability of nonlocal Sobolev inequality

Advanced Nonlinear Studies
This 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
doaj   +1 more source

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.
openaire   +2 more sources