在非自然指数下Beltrami方程的Lp可积性

数学物理学报 ›› 1998, Vol. 18 ›› Issue (S1): 13-20.

在非自然指数下Beltrami方程的L^p可积性

郑神州

北方交通大学数学系北京 100044

收稿日期:1996-03-25 修回日期:1996-09-23 出版日期:1998-12-26 发布日期:1998-12-26
基金资助:
国家自然科学基金资助项目

The L^p -integrability of Beltrami's Equations with Non-natural Exponents

Zheng Shenzhou

Department of Mathematics North Jiaotong Unrvsity, Beijing 100044

Received:1996-03-25 Revised:1996-09-23 Online:1998-12-26 Published:1998-12-26

摘要/Abstract

摘要： 对于n维的 Beltrami方程,存在指数 r₁和r₂,满足1 < r₁ < n < r₂ < ∞,使得方程在非自然指数Sobolev空间W_loc¹(Ω,Rⁿ)中的弱解f(x),都有f(x)∈W_loc²(Ω,Rⁿ).

关键词: 弱K-拟正则映射, Beltrami方程向量场的分解, 逆Hölder不等式

Abstract: For Beltrami's equations in Rⁿ,n ≥ 2,there exist two exponents r₁,r₂, which satisfy1 < r₁ < n < r₂ < ∞,such that every weakly solution f(x) of Beltrami's equations in W_loc^1,r₁(Ω,Rⁿ) belongs to W_loc^1,r₂(Ω,Rⁿ).

Key words: Weakly K-quasiregular mappings, Beltrami's equations, the deoom position of vector field, reverse Hölder's inequality

郑神州. 在非自然指数下Beltrami方程的L^p可积性[J]. 数学物理学报, 1998, 18(S1): 13-20.

Zheng Shenzhou. The L^p -integrability of Beltrami's Equations with Non-natural Exponents[J]. Acta mathematica scientia,Series A, 1998, 18(S1): 13-20.