UNIQUENESS OF SOLUTIONS FOR SOME ELLIPTIC EQUATIONS WITH A QUADRATIC GRADIENT TERM

被引：40

作者：

Arcoya, David ^{[1
]}

Segura de Leon, Sergio ^{[2
]}

机构：

[1] Univ Granada, Dept Anal Matemat, E-18071 Granada, Spain

[2] Univ Valencia, Dept Anal Matemat, E-46100 Valencia, Spain

来源：

ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS | 2010年 / 16卷 / 02期

关键词：

Non linear elliptic problems; uniqueness; comparison principle; lower order terms with singularities at the Gradient term; lack of coerciveness; QUASI-LINEAR EQUATIONS; LOWER ORDER TERM; UNBOUNDED SOLUTIONS; GROWTH;

D O I：

10.1051/cocv:2008072

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

We study a comparison principle and uniqueness of positive solutions for the homogeneous Dirichlet boundary value problem associated to quasi-linear elliptic equations with lower order terms. A model example is given by -Delta u + lambda vertical bar Delta u vertical bar(2)/u(r) = f(x), lambda,r > 0. The main feature of these equations consists in having a quadratic gradient term in which singularities are allowed. The arguments employed here also work to deal with equations having lack of ellipticity or some dependence on u in the right hand side. Furthermore, they could be applied to obtain uniqueness results for nonlinear equations having the p-Laplacian operator as the principal part. Our results improve those already known, even if the gradient term is not singular.

引用

页码：327 / 336

页数：10

共 30 条

[1]

Adams R., 1985, Sobolev Spaces

[2] Existence results for nonlinear elliptic equations with degenerate coercivity [J].