A note on a critical problem with natural growth in the gradient

Abdellaoui, Boumediene, and Peral, Ireneo. "A note on a critical problem with natural growth in the gradient." Journal of the European Mathematical Society 008.2 (2006): 157-170. <http://eudml.org/doc/277788>.

@article{Abdellaoui2006,
abstract = {The paper analyzes the influence on the meaning of natural growth in the gradient of a perturbation by a Hardy potential in some elliptic equations. Indeed, in the case of the Laplacian the natural problem becomes $−\Delta u−\Lambda _N\frac\{u\}\{|x|^2\}=\left|\nabla u+\frac\{N−2\}\{2\}\frac\{u\}\{|x|^2\}x\right|^2|x|^\{(N−2)/2\}+\lambda f(x)$ in $\Omega $, $u=0$ on $\partial \Omega $, $\Lambda _N=((N−2)/2)^2$. This problem is a particular case of problem (2). Notice that $(N−2)/2$ is optimal as coefficient and exponent on the right hand side.},
author = {Abdellaoui, Boumediene, Peral, Ireneo},
journal = {Journal of the European Mathematical Society},
keywords = {elliptic equations; Hardy potential; quadratic growth in the gradient; optimal summability; elliptic equations; Hardy potential; quadratic growth in the gradient; optimal summability},
language = {eng},
number = {2},
pages = {157-170},
publisher = {European Mathematical Society Publishing House},
title = {A note on a critical problem with natural growth in the gradient},
url = {http://eudml.org/doc/277788},
volume = {008},
year = {2006},
}

TY - JOUR
AU - Abdellaoui, Boumediene
AU - Peral, Ireneo
TI - A note on a critical problem with natural growth in the gradient
JO - Journal of the European Mathematical Society
PY - 2006
PB - European Mathematical Society Publishing House
VL - 008
IS - 2
SP - 157
EP - 170
AB - The paper analyzes the influence on the meaning of natural growth in the gradient of a perturbation by a Hardy potential in some elliptic equations. Indeed, in the case of the Laplacian the natural problem becomes $−\Delta u−\Lambda _N\frac{u}{|x|^2}=\left|\nabla u+\frac{N−2}{2}\frac{u}{|x|^2}x\right|^2|x|^{(N−2)/2}+\lambda f(x)$ in $\Omega $, $u=0$ on $\partial \Omega $, $\Lambda _N=((N−2)/2)^2$. This problem is a particular case of problem (2). Notice that $(N−2)/2$ is optimal as coefficient and exponent on the right hand side.
LA - eng
KW - elliptic equations; Hardy potential; quadratic growth in the gradient; optimal summability; elliptic equations; Hardy potential; quadratic growth in the gradient; optimal summability
UR - http://eudml.org/doc/277788
ER -