Convex domains and unique continuation at the boundary

被引：1

作者：

Adolfsson, Vilhelm ^{[1
]}

Escauriaza, Luis ^{[2
]}

Kenig, Carlos ^{[3
]}

机构：

[1] CTH, Matemat Inst, S-41296 Gothenburg, Sweden

[2] Univ Pais Vasco, Dept Matemat, Leioa 48080, Spain

[3] Univ Chicago, Dept Math, Chicago, IL 60637 USA

来源：

REVISTA MATEMATICA IBEROAMERICANA | 1995年 / 11卷 / 03期

关键词：

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show that a harmonic function which vanishes continuously on an open set of the boundary of a convex domain cannot have a normal derivative which vanishes on a subset of positive surface measure. We also prove a similar result for caloric functions vanishing on the lateral boundary of a convex cylinder.

引用

页码：513 / 525

页数：13

共 7 条

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[2]

DAHLBERG BEJ, 1977, ARCH RATION MECH AN, V65, P276

[3] ESTIMATES OF CALORIC MEASURE AND THE INITIAL-DIRICHLET PROBLEM FOR THE HEAT-EQUATION IN LIPSCHITZ CYLINDERS [J].

FABES, E ;

SALSA, S .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1983, 279 (02) :635-650

[4]

Gilbarg D., 1977, GRUNDLEHREN MATH WIS, V224, DOI DOI 10.1007/978-3-642-61798-0

[5]

Lin Fang Hua, 1991, COMMUN PUR APPL MATH, V45, P287

[6]

Lin Fang Hua, 1990, COMMUN PUR APPL MATH, V43, P127

[7]

Wolff, 1990, C MATH, V60, P253, DOI 10.4064/cm-60-61-1-253-260

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