STABILITY OF MAPPINGS WITH BOUNDED DISTORTION IN THE SOBOLEV NORM ON THE JOHN DOMAINS OF HEISENBERG GROUPS

Isangulova DV

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STABILITY OF MAPPINGS WITH BOUNDED DISTORTION IN THE SOBOLEV NORM ON THE JOHN DOMAINS OF HEISENBERG GROUPS

机译：海森堡群的JOHN Domain上的Sobolev范数中有界畸变的映射的稳定性

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This article completes the authors's series on stability in the Liouville theorem on the Heisenberg group. We show that every mapping with bounded distortion on a John domain of the Heisenberg group is approximated by a conformal mapping with order of closeness root K-1 in the uniform norm and with order of closeness K-1 in the Sobolev L1/p-norm for all p < C/K-1. We construct two examples, demonstrating the asymptotic sharpness of our results.

机译：本文完成了作者在Heisenberg群上的Liouville定理中关于稳定性的系列。我们表明，在海森堡群的John域上每个有界畸变的映射都由一个保形映射来逼近，该保形映射在统一范数中具有接近度根K-1，在Sobolev L1 / p-范数中具有接近度K-1。对于所有p

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来源
《Siberian Mathematical Journal》 |2009年第3期|共19页
作者
Isangulova DV;
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原文格式 PDF
正文语种 eng
中图分类数学;
关键词
Heisenberg group; mapping with bounded distortion; John domain; Mobius; transformation;

机译：Heisenberg群;有界变形映射;John域;Mobius;变换;

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专利

1. STABILITY OF MAPPINGS WITH BOUNDED DISTORTION IN THE SOBOLEV NORM ON THE JOHN DOMAINS OF HEISENBERG GROUPS [J] . Isangulova DV Siberian Mathematical Journal . 2009,第3期

机译：海森堡群的JOHN Domain上的Sobolev范数中有界畸变的映射的稳定性
2. Linear Image Reconstruction by Sobolev Norms on the Bounded Domain [J] . Janssen BJ, Duits R International Journal of Computer Vision . 2009,第2期

机译：Sobolev范数在有界域上的线性图像重构
3. Linear Image Reconstruction by Sobolev Norms on the Bounded Domain [J] . Bart J. Janssen, Remco Duits International Journal of Computer Vision . 2009,第2期

机译：Sobolev范数在有界域上的线性图像重构
4. Linear Image Reconstruction by Sobolev Norms on the Bounded Domain [C] . Bart Janssen, Remco Duits, Bart ter Haar Romeny Scale Space and Variational Methods in Computer Vision; Lecture Notes in Computer Science; 4485 . 2007

机译：Sobolev范数在有界域上的线性图像重构
5. Sobolev-type Embedding on Cauchy-Riemann Manifolds and Nonlinear Sub-elliptic PDE on Heisenberg Group [D] . Shi, Xiaojie. 2018

机译：Cauchy-Riemann流形上的Sobolev型嵌入和Heisenberg群上的非线性亚椭圆PDE
6. Estimation of Sobolev embedding constant on a domain dividable into bounded convex domains [O] . Makoto Mizuguchi, Kazuaki Tanaka, Kouta Sekine, -1

机译：可分为有界凸域的域上Sobolev嵌入常数的估计
7. Linear Image Reconstruction by Sobolev Norms on the Bounded Domain [O] . Bart Janssen, Remco Duits 2013

机译：sobolev范数在有界域上的线性图像重建

STABILITY OF MAPPINGS WITH BOUNDED DISTORTION IN THE SOBOLEV NORM ON THE JOHN DOMAINS OF HEISENBERG GROUPS

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