Geodesic
Second-order boundary estimates for solutions to singular elliptic equations in borderline cases
Electronic Journal of Differential Equations, Tome 2011 (2011).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: Let $\Omega\subset R^N$ be a bounded smooth domain. We investigate the effect of the mean curvature of the boundary $\partial\Omega$ on the behaviour of the solution to the homogeneous Dirichlet boundary value problem for the equation $\Delta u+f(u)=0$. Under appropriate growth conditions on $f(t)$ as t approaches zero, we find asymptotic expansions up to the second order of the solution in terms of the distance from x to the boundary $\partial\Omega$.
Classification : 35B40, 35J67
Keywords: elliptic problems, singular equations, second order boundary approximation 
@article{EJDE_2011__2011__a73,
     author = {Anedda, Claudia and Porru, Giovanni},
     title = {Second-order boundary estimates for solutions to singular elliptic equations in borderline cases},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2011},
     year = {2011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2011__2011__a73/}
}
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Anedda, Claudia; Porru, Giovanni. Second-order boundary estimates for solutions to singular elliptic equations in borderline cases. Electronic Journal of Differential Equations, Tome 2011 (2011). http://geodesic.mathdoc.fr/item/EJDE_2011__2011__a73/