On the porosity of free boundaries in degenerate variational inequalities

被引：41

作者：

Karp, L

Kilpeläinen, T

Petrosyan, A

Shahgholian, H

机构：

[1] Int Coll Technol, Dept Appl Math, IL-20101 Karmiel, Israel

[2] Univ Jyvaskyla, Dept Math, Jyvaskyla 40351, Finland

[3] Royal Inst Technol, Dept Math, S-10044 Stockholm, Sweden

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2000年 / 164卷 / 01期

基金：

芬兰科学院;

关键词：

obstacle problem; nonhomogeneous p-Laplace equation; free boundary; porosity;

D O I：

10.1006/jdeq.1999.3754

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this note we consider a certain degenerate variational problem with constraint identically zero. The exact growth of the solution near th free boundary is established. A consequence of this is that the free boundary is porous and therefore its Hausdorff dimension is less than N and hence it is of Lebesgue measure zero. (C) 2000 Academic Press.

引用

页码：110 / 117

页数：8

共 7 条

[1] CAFFARELLI LA, 1980, COMMUN PART DIFF EQ, V5, P427
[2] ON THE OBSTACLE PROBLEM FOR QUASI-LINEAR ELLIPTIC-EQUATIONS OF P LAPLACIAN TYPE
CHOE, HJ
LEWIS, JL
[J]. SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 1991, 22 (03) : 623 - 638
[3] HOLDER CONTINUITY OF THE GRADIENT FOR DEGENERATE VARIATIONAL-INEQUALITIES
FUCHS, M
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1990, 15 (01) : 85 - 100
[4] Heinonen J., 1993, NONLINEAR POTENTIAL
[5] MARTIO O, 1987, EXPO MATH, V5, P17
[6] SMOOTH REGULARITY OF SOLUTIONS OF DOUBLE OBSTACLE PROBLEMS INVOLVING DEGENERATE ELLIPTIC-EQUATIONS
MU, J
ZIEMER, WP
[J]. COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 1991, 16 (4-5) : 821 - 843
[7] LOCAL BEHAVIOR OF SOLUTIONS OF QUASI-LINEAR EQUATIONS
SERRIN, J
[J]. ACTA MATHEMATICA, 1964, 111 (3-4) : 247 - 302

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