Volume 16, Number 2, April-June 2010
|Page(s)||327 - 336|
|Published online||19 December 2008|
Uniqueness of solutions for some elliptic equations with a quadratic gradient term
Departamento de Análisis Matemático,
Universidad de Granada,
Campus Fuentenueva s/n, 18071 Granada, Spain. firstname.lastname@example.org
2 Departament d'Anàlisi Matemàtica, Universitat de València, Dr. Moliner 50, 46100 Burjassot, Valencia, Spain. email@example.com
Revised: 2 October 2008
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
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.
Mathematics Subject Classification: 35J65 / 35J70 / 35J60
Key words: Non linear elliptic problems / uniqueness / comparison principle / lower order terms with singularities at the Gradient term / lack of coerciveness
© EDP Sciences, SMAI, 2008
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