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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.
Keywords: non linear elliptic problems, uniqueness, comparison principle, lower order terms with singularities at the gradient term, lack of coerciveness
@article{COCV_2010__16_2_327_0,
author = {Arcoya, David and Segura de Le\'on, Sergio},
title = {Uniqueness of solutions for some elliptic equations with a quadratic gradient term},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {327--336},
publisher = {EDP-Sciences},
volume = {16},
number = {2},
year = {2010},
doi = {10.1051/cocv:2008072},
mrnumber = {2654196},
zbl = {1189.35109},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv:2008072/}
}
TY - JOUR AU - Arcoya, David AU - Segura de León, Sergio TI - Uniqueness of solutions for some elliptic equations with a quadratic gradient term JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2010 SP - 327 EP - 336 VL - 16 IS - 2 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/cocv:2008072/ DO - 10.1051/cocv:2008072 LA - en ID - COCV_2010__16_2_327_0 ER -
%0 Journal Article %A Arcoya, David %A Segura de León, Sergio %T Uniqueness of solutions for some elliptic equations with a quadratic gradient term %J ESAIM: Control, Optimisation and Calculus of Variations %D 2010 %P 327-336 %V 16 %N 2 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/cocv:2008072/ %R 10.1051/cocv:2008072 %G en %F COCV_2010__16_2_327_0
Arcoya, David; Segura de León, Sergio. Uniqueness of solutions for some elliptic equations with a quadratic gradient term. ESAIM: Control, Optimisation and Calculus of Variations, Tome 16 (2010) no. 2, pp. 327-336. doi: 10.1051/cocv:2008072
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