Some estimates for the dipolar Loewner differential equation

DU Zhenye; LAN Shiyi

doi:10.13471/j.cnki.acta.snus.2020.06.18.2020A027

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Some estimates for the dipolar Loewner differential equation

Research articles | 更新时间：2023-11-01

- Some estimates for the dipolar Loewner differential equation
- Acta Scientiarum Naturalium Universitatis Sunyatseni Vol. 60, Issue 5, Pages: 175-184(2021)
- 作者机构：
  
  广西民族大学数学与物理学院，广西南宁 530006
- 作者简介：
- 基金信息：
- DOI：10.13471/j.cnki.acta.snus.2020.06.18.2020A027
  CLC： O175
- Published：25 September 2021，
  
  Published Online：19 March 2021，
  
  Received：18 June 2020，
  
  Accepted：11 November 2020
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杜振叶,蓝师义.偶极Loewner微分方程的一些估计[J].中山大学学报(自然科学版),2021,60(05):175-184.

DU Zhenye,LAN Shiyi.Some estimates for the dipolar Loewner differential equation[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2021,60(05):175-184.
杜振叶,蓝师义.偶极Loewner微分方程的一些估计[J].中山大学学报(自然科学版),2021,60(05):175-184. DOI： 10.13471/j.cnki.acta.snus.2020.06.18.2020A027.

DU Zhenye,LAN Shiyi.Some estimates for the dipolar Loewner differential equation[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2021,60(05):175-184. DOI： 10.13471/j.cnki.acta.snus.2020.06.18.2020A027.

摘要

Loewner微分方程是一种产生Loewner链的偏微分方程。首先，应用Bieberbach定理给出了偶极Loewner微分方程的解关于时间方向变化的一个估计；其次，基于逆时间的Loewner微分方程导出了对应于两个不同驱动函数的偶极Loewner微分方程的解的差值可以通过这两个驱动函数差的上确界范数来估计。这将通弦与径向Loewner微分方程的一些相应结果推广到偶极Loewner微分方程。

Abstract

The Loewner differential equation is a partial differential equation that generates a Loewner chain. An estimation of the solution of the dipolar Loewner differential equation for time-direction is first derived by using Bieberbach theorem.Based on the reverse-time Loewner equation the difference of two solutions to the dipolar Loewner equation with two different deriving functions is estimated in terms of the supremum norm of the difference of the two driving functions. This generalizes some related results for the chordal and radial Loewner equations to the dipolar setting.

关键词

Loewner微分方程驱动函数随机Loewner演变（SLE）

Keywords

Loewner differential equationdriving functionstochastic Loewner evolution （SLE）

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