Isolated boundary singularities of semilinear elliptic equations

Given a smooth domain Omega subset of R-N such that 0 is an element of partial derivative Omega and given a nonnegative smooth function zeta on partial derivative Omega, we study the behavior near 0 of positive solutions of -Delta u = u(q) in Omega such that u = zeta on partial derivative Omega{0}. We prove that if N+1/N-1 < q < N-2/N-2, then u(x) <= C broken vertical bar x broken vertical bar(-2/q-1) and we compute the limit of broken vertical bar x broken vertical bar(-2/q-1)u(x) as x -> 0. We also investigate the case q = N+1/N-1 . The proofs rely on the existence and uniqueness of solutions of related equations on spherical domains.