Second-order boundary estimates for solutions to singular elliptic equations in borderline cases

Anedda Claudia;Porru Giovanni

2011-01-01

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Abstract

Let \Omega \subsetR^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.