On singular sets of local solutions to p-Laplace equations

被引：51

作者：

Lou, Hongwei ^{[1
]}

机构：

[1] Fudan Univ, Sch Math Sci, Key Lab Math Nonlinear Sci, Shanghai 200433, Peoples R China

来源：

CHINESE ANNALS OF MATHEMATICS SERIES B | 2008年 / 29卷 / 05期

基金：

中国国家自然科学基金;

关键词：

singular set; p-Laplace equation; optimal control; existence;

D O I：

10.1007/s11401-007-0312-y

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The author proves that the right-hand term of a p-Laplace equation is zero on the singular set of a local solution to the equation. Such a result is used to study the existence of an optimal control problem.

引用

页码：521 / 530

页数：10

共 10 条

[1] DISTRIBUTED CONTROL OF SYSTEMS GOVERNED BY A GENERAL-CLASS OF QUASI-LINEAR ELLIPTIC-EQUATIONS [J].

CASAS, E ;

FERNANDEZ, LA .

JOURNAL OF DIFFERENTIAL EQUATIONS, 1993, 104 (01) :20-47

[2] C1+ALPHA LOCAL REGULARITY OF WEAK SOLUTIONS OF DEGENERATE ELLIPTIC-EQUATIONS [J].

DIBENEDETTO, E .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1983, 7 (08) :827-850

[3]

Gilbarg D., 1998, Elliptic Partial Differential Equations of Second Order, V2nd ed.

[4]

KINDERLEHRER D, 1981, INTRO VARIATIONAL IN

[5] Existence of optimal controls for semilinear elliptic equations without Cesari-type conditions [J].

Lou, HW .

ANZIAM JOURNAL, 2003, 45 :115-131

[6] Existence of optimal controls for semilinear parabolic equations without Cesari-type conditions [J].

Lou, HW .

APPLIED MATHEMATICS AND OPTIMIZATION, 2003, 47 (02) :121-142

[7]

Morrey C. B. J., 1961, EXISTENCE DIFFERENTI, P241

[8] ON HARNACKS THEOREM FOR ELLIPTIC DIFFERENTIAL EQUATIONS [J].

MOSER, J .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1961, 14 (03) :577-&

[9] REGULARITY FOR A MORE GENERAL-CLASS OF QUASILINEAR ELLIPTIC-EQUATIONS [J].

TOLKSDORF, P .

JOURNAL OF DIFFERENTIAL EQUATIONS, 1984, 51 (01) :126-150

[10]

Troianiello G.M., 1987, ELLIPTIC DIFFERENTIA

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