Carleman Estimates and Unique Continuation for Second Order Parabolic Equations with Nonsmooth Coefficients

被引：54

作者：

Koch, Herbert ^{[1
]}

Tataru, Daniel ^{[2
]}

机构：

[1] Univ Bonn, Math Inst, D-53115 Bonn, Germany

[2] Univ Calif Berkeley, Dept Math, Berkeley, CA 94720 USA

来源：

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS | 2009年 / 34卷 / 04期

关键词：

Carleman estimates; Parabolic equations; Strong unique continuation; ELLIPTIC DIFFERENTIAL-EQUATIONS; HERMITE EXPANSIONS; HEAT OPERATOR; THEOREM; INEQUALITIES; SUMMABILITY;

D O I：

10.1080/03605300902740395

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this work we obtain strong unique continuation results for variable coefficient second order parabolic equations. The coefficients in the principal part are assumed to satisfy a Lipschitz condition in x and a Holder [image omitted] condition in time. The coefficients in the lower order terms, i.e., the potential and the gradient potential, are allowed to be unbounded and required only to satisfy mixed norm bounds in scale invariant [image omitted] spaces.

引用

页码：305 / 366

页数：62

共 35 条

[1] LOCAL BEHAVIOR OF SOLUTIONS TO PARABOLIC EQUATIONS [J].