Second-order boundary estimates for solutions to singular elliptic equations in borderline cases
Claudia Anedda, Giovanni Porru · UNICA IRIS Institutional Research Information System (University of Cagliari) · 2011
Let $Omegasubset R^N$ be a bounded smooth domain. We investigate the effect of the mean curvature of the boundary $partialOmega$ 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 $partialOmega$.