Second-order boundary estimates for solutions to singular elliptic equations

ANEDDA, CLAUDIA

2009-01-01

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Abstract

Let ω ⊂ R N be a bounded smooth domain. We investigate the effect of the mean curvature of the boundary ∂ω in the behaviour of the solution to the homogeneous Dirichlet boundary value problem for the singular semilinear equation δu + f(u) = 0. Under appropriate growth conditions on f(t) as t approaches zero, we find an asymptotic expansion up to the second order of the solution in terms of the distance from x to the boundary ∂ ω .