Improving sharp sobolev type inequalities by optimal remainder gradient norms

Cianchi A.; Ferone A.

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Improving sharp sobolev type inequalities by optimal remainder gradient norms

机译：通过最优余数梯度范数改善尖锐的Sobolev型不等式

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摘要

We are concerned with Sobolev type inequalities in W _0 ~(1,P);(Ω), Ω ? ? ~n, with optimal target norms and sharp constants. Admissible remainder terms depending on the gradient are characterized. As a consequence, the strongest possible remainder norm of the gradient is exhibited. Both the case when p < n and the borderline case when p = n are considered. Related Hardy inequalities with remainders are also derived.

机译：我们关注W _0〜（1，P）;（Ω），Ω？中的Sobolev型不等式。？〜n，具有最佳目标规范和尖锐常数。根据梯度确定了可允许的余项。结果，显示出梯度的最大可能余数范数。同时考虑p

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《Communications on pure and applied analysis》 |2012年第3期|共24页
作者
Cianchi A.; Ferone A.;
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正文语种 eng
中图分类数学;
关键词
Hardy-Sobolev inequality; Lorentz spaces; Rearrangement invariant spaces; Remainder terms;

机译：Hardy-Sobolev不等式;Lorentz空间;重排不变空间;余项;

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1. Improving sharp sobolev type inequalities by optimal remainder gradient norms [J] . Cianchi A., Ferone A. Communications on pure and applied analysis . 2012,第3期

机译：通过最优余数梯度范数改善尖锐的Sobolev型不等式
2. Sharp Hardy-Sobolev Inequalities with General Weights and Remainder Terms [J] . Yaotian Shen, Zhihui Chen Journal of inequalities and applications . 2009,第pta3期

机译：具有权重和余项的Sharp Hardy-Sobolev不等式
3. Sharp Hardy-Sobolev Inequalities with General Weights and Remainder Terms [J] . Yaotian Shen, Zhihui Chen Journal of inequalities and applications . 2009,第1期

机译：具有一般权重和余项的Sharp Hardy-Sobolev不等式
4. Heat Kernel Estimates, Sobolev-Type Inequalities and Riesz Transform on Noncompact Riemannian Manifolds [C] . Thierry Coulhon SMS 2011 . 2013

机译：热内核估计，SoboLev型不等式和Riesz变换在非媒体riemannian歧管上
5. Multiwavelet based method of moments under discrete Sobolev-type norm. [D] . Tong, Meisong. 2004

机译：离散Sobolev型模下基于多小波的矩法。
6. Hardy type inequalities in ... formula ... with sharp remainders [O] . Norisuke Ioku, Michinori Ishiwata, Tohru Ozawa -1

机译：...公式...中的Hardy型不等式具有明显的余数
7. Sharp Hardy-Sobolev Inequalities with General Weights and Remainder Terms [O] . 2009

机译：具有权重和余项的Sharp Hardy-Sobolev不等式
8. Sobolev-Poincare's Inequality and the Neumann Problem for u sub t = Divergence of the Absolute Value of the Gradient u to the P-2 Power x the Gradient u [R] . Fukuda, I. 1985

机译：sobolev-poincare的不等式和u sub的Neumann问题t =梯度u的绝对值与p-2幂的差异x梯度u

Improving sharp sobolev type inequalities by optimal remainder gradient norms

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