The obstacle problem for nonlinear elliptic equations with variable growth and L1-data

被引：39

作者：

Rodrigues, Jose Francisco ^{[1
,2
]}

Sanchon, Manel ^{[3
]}

Urbano, Jose Miguel ^{[3
]}

机构：

[1] Univ Coimbra, Dept Math, CMUC, Coimbra, Portugal

[2] Univ Lisbon, FCUL, P-1649003 Lisbon, Portugal

[3] Univ Coimbra, Dept Math, CMUC, P-3001454 Coimbra, Portugal

来源：

MONATSHEFTE FUR MATHEMATIK | 2008年 / 154卷 / 04期

关键词：

obstacle problem; variable growth; entropy solutions; L-1-data; Lewy-Stampacchia inequalities; stability;

D O I：

10.1007/s00605-008-0550-4

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The aim of this paper is twofold: to prove, for L-1-data, the existence and uniqueness of an entropy solution to the obstacle problem for nonlinear elliptic equations with variable growth, and to show some convergence and stability properties of the corresponding coincidence set. The latter follow from extending the Lewy-Stampacchia inequalities to the general framework of L-1.

引用

页码：303 / 322

页数：20

共 33 条

[1] Regularity results for a class of functionals with non-standard growth [J].