On the Unique Continuation Properties for Elliptic Operators with Singular Potentials

被引：0
作者：
Xiang Xing Tao
Song Yan Zhang
机构：
[1] Faculty of Science,Department of Mathematics
[2] Ningbo University,undefined
来源：
Acta Mathematica Sinica, English Series | 2007年 / 23卷
关键词：
doubling property; unique continuation; Lipschitz domain; Kato–Fefferman–Phong’s potential; 35B60; 35R05; 42B20;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
Let u be a solution to a second order elliptic equation with singular potentials belonging to Kato–Fefferman–Phong’s class in Lipschitz domains. An elementary proof of the doubling property for u2 over balls is presented, if the balls are contained in the domain or centered at some points near an open subset of the boundary on which the solution u vanishes continuously. Moreover, we prove the inner unique continuation theorems and the boundary unique continuation theorems for the elliptic equations, and we derive the ℬp weight properties for the solution u near the boundary.
引用
收藏
页码：297 / 308
页数：11
相关论文
共 17 条
  • [1] Simon undefined(1982)undefined Bull. Amer. Math. Soc. 7 447-undefined
  • [2] Carleman undefined(1939)undefined Ark. Mat. 26B 1-undefined
  • [3] Jerison undefined(1985)undefined Ann. of Math. 121 463-undefined
  • [4] Aizenman undefined(1982)undefined Comm. Pure Appl. Math. 35 209-undefined
  • [5] Chiarenza undefined(1986)undefined Proc. Amer. Soc. 98 415-undefined
  • [6] Garofalo undefined(1986)undefined Indiana Univ. Math. J. 35 245-undefined
  • [7] Garofalo undefined(1987)undefined Comm. pure Appl. Math. 40 347-undefined
  • [8] Fabes undefined(1990)undefined J. Func. Anal. 88 194-undefined
  • [9] Kurata undefined(1993)undefined Commun. in Partial Differential Equations 18 1161-undefined
  • [10] Kurata undefined(1997)undefined Pro. Amer. Soc. Math. 125 853-undefined
12