Results 91 to 100 of about 1,128 (190)

Stability for the Sobolev inequality in cones

Journal of Differential Equations
We prove a quantitative Sobolev inequality in cones of Bianchi-Egnell type, which implies a stability property. Our result holds for any cone as long as the minimizers of the Sobolev quotient are nondegenerate, which is the case of most cones. When the minimizers are the classical bubbles we have more precise results.
Giulio Ciraolo, Filomena Pacella, Camilla Chiara Polvara   +2 more
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Sharp radial Sobolev inequalities with inverse square potentials and applications to nonlinear Schrödinger equations

Journal of Inequalities and Applications
We prove the sharp radial Sobolev inequality with a repulsive inverse square potential. Considered all H ˙ 1 $\dot{H}^{1} $ functions, the inequality is not attained by non-trivial function.
Masaru Hamano, Masahiro Ikeda
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On weighted Calderón-Zygmund singular integrals and applications

Journal of Innovative Applied Mathematics and Computational Sciences, 2022
This paper studies some weighted norm inequalities related to some Calderon-Zygmund singular integrals. Applications to the Sobolev-Gagliardo-Nirenberg inequality, differential forms, and the potential equation du = f are given.
Ahmed Loulit
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Maximizers for the Strichartz and the Sobolev-Strichartz inequalities for the Schrodinger equation

Electronic Journal of Differential Equations, 2009
In this paper, we first show that there exists a maximizer for the non-endpoint Strichartz inequalities for the Schrodinger equation in all dimensions based on the recent linear profile decomposition result.
Shuanglin Shao
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Blowup of Smooth Solutions for an Aggregation Equation

Abstract and Applied Analysis, 2013
We study the blowup criterion of smooth solutions for an inviscid aggregation equation in . By means of the losing estimates and the logarithmic Sobolev inequality, we establish an improved blowup criterion of smooth solutions.
Wenxin Yu, Yigang He
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On weighted Orlicz-Sobolev inequalities

Discrete and Continuous Dynamical Systems
Let $Ω$ be an open subset of $\mathbb{R}^N$ with $N\geq 2.$ We identify various classes of Young functions $Φ$ and $Ψ$, and function spaces for a weight function $g$ so that the following weighted Orlicz-Sobolev inequality holds: \begin{equation*}\label{ineq:Orlicz} Ψ^{-1}\left(\int_Ω|g(x)|\,Ψ(|u(x)| )dx \right)\leq CΦ^{-1}\left(\int_ΩΦ(|\nabla u(x ...
Anoop, T. V., Das, Ujjal, Roy, Subhajit
openaire   +2 more sources

Riesz Potential on the Heisenberg Group

Journal of Inequalities and Applications, 2011
The relation between Riesz potential and heat kernel on the Heisenberg group is studied. Moreover, the Hardy-Littlewood-Sobolev inequality is established.
Xiao Jinsen, He Jianxun
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On a singular anisotropic parabolic equation related to the p → ( x ) $\vec{p}(x)$ -Laplacian

Boundary Value Problems
This paper investigates a singular anisotropic parabolic equation associated with the p i ( x ) $p_{i}(x)$ -Laplacian operator. By employing the anisotropic Gagliardo-Sobolev-Nirenberg inequality and a modified Di Giorgi iteration technique, we derive a ...
Qitong Ou, Huashui Zhan
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Complete positivity order and relative entropy decay

Forum of Mathematics, Sigma
We prove that for a GNS-symmetric quantum Markov semigroup, the complete modified logarithmic Sobolev constant is bounded by the inverse of its complete positivity mixing time.
Li Gao, Marius Junge, Nicholas LaRacuente, Haojian Li   +3 more
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The Best Constant of Sobolev Inequality Corresponding to Clamped Boundary Value Problem

Boundary Value Problems, 2011
Green's function of the clamped boundary value problem for the differential operator on the interval is obtained. The best constant of corresponding Sobolev inequality is given by .
Kametaka Yoshinori, Nagai Atsushi, Takemura Kazuo, Yamagishi Hiroyuki, Watanabe Kohtaro   +4 more
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