Results 31 to 40 of about 6,369 (172)
On Scales of Sobolev spaces associated to generalized Hardy operators
, 2021 We consider the fractional Laplacian with Hardy potential and study the scale of homogeneous $L^p$ Sobolev spaces generated by this operator. Besides generalized and reversed Hardy inequalities, the analysis relies on a H\"ormander multiplier theorem ...
Merz, Konstantin
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Hypoelliptic functional inequalities [PDF]
, 2018 In this paper we derive a variety of functional inequalities for general homogeneous invariant hypoelliptic differential operators on nilpotent Lie groups.
Ruzhansky, Michael +1 more
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Extremals in Hardy-Littlewood-Sobolev inequalities for stable processes
Journal of Mathematical Analysis and Applications, 2022 We prove the existence of an extremal function in the Hardy-Littlewood-Sobolev inequality for the energy associated to an stable operator. To this aim we obtain a concentration-compactness principle for stable processes in $\mathbb{R}^N$.
de Pablo, Arturo +2 more
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Choquard-type equations with Hardy–Littlewood–Sobolev upper-critical growth
Advances in Nonlinear Analysis, 2018 We are concerned with the existence of ground states and qualitative properties of solutions for a class of nonlocal Schrödinger equations. We consider the case in which the nonlinearity exhibits critical growth in the sense of the Hardy–Littlewood ...
Cassani Daniele, Zhang Jianjun
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Existence of positive solutions to negative power nonlinear integral equations with weights
Boundary Value Problems, 2020 This paper is devoted to the existence and non-existence of positive solutions to the following negative power nonlinear integral equation related to the sharp reversed Hardy–Littlewood–Sobolev inequality: f q − 1 ( x ) = ∫ Ω K ( x ) f ( y ) K ( y ) | x −
Hang Chen, Qianqiao Guo, Qian Wang
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Biharmonic system with Hartree-type critical nonlinearity
Electronic Journal of Qualitative Theory of Differential Equations, 2023 In this article, we investigate the multiplicity results of the following biharmonic Choquard system involving critical nonlinearities with sign-changing weight function: \begin{align*} \begin{cases} \Delta^{2}u = \lambda F(x) |u|^{r-2}u+ H(x)\left ...
Anu Rani, Sarika Goyal
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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 +2 more
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On the critical Choquard-Kirchhoff problem on the Heisenberg group
Advances in Nonlinear Analysis, 2022 In this paper, we deal with the following critical Choquard-Kirchhoff problem on the Heisenberg group of the form: M(‖u‖2)(−ΔHu+V(ξ)u)=∫HN∣u(η)∣Qλ∗∣η−1ξ∣λdη∣u∣Qλ∗−2u+μf(ξ,u),M\left(\Vert u{\Vert }^{2})\left(-{\Delta }_{{\mathbb{H}}}u\left+V\left(\xi )u)=\
Sun Xueqi, Song Yueqiang, Liang Sihua
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Probabilistic Approach to Fractional Integrals and the Hardy-Littlewood-Sobolev Inequality
, 2013 We give a short summary of Varopoulos' generalised Hardy-Littlewood-Sobolev inequality for self-adjoint $C_{0}$ semigroups and give a new probabilistic representation of the classical fractional integral operators on $\R^n$ as projections of martingale ...
Applebaum, David, Banuelos, Rodrigo
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Affine Hardy–Littlewood–Sobolev inequalities
Journal of the European Mathematical SocietySharp 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
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