Some results on the qualitative properties of positive solutions of quasilinear elliptic equations

被引：30
|
作者：
Sciunzi, Berardino [1 ]
机构：
[1] Univ Roma Tor Vergata, Dipartimento Matemat, I-00133 Rome, Italy
来源：
NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS | 2007年 / 14卷 / 3-4期
关键词：
m-Laplace operator; geometric and qualitative properties of the solutions; regularity of the solutions;
D O I：
10.1007/s00030-007-5047-7
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We consider the Dirichlet problem -Delta(m)- (u) = f (u) in Omega with zero Dirichlet boundary conditions. We prove local summability properties of 1/vertical bar Du vertical bar and we exploit these results to give geometric characterizations of the critical set Z = { x is an element of Omega vertical bar Du(x) = 0}. We extend to the case of changing sign nonlinearities some results known in the case f (s) > 0 for s > 0.
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页码：315 / 334
页数：20
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