Boundary blow-up solutions in the unit ball : asymptotics, uniqueness and symmetry

We calculate the full asymptotic expansion of boundary blow-up so- lutions, for any nonlinearity f . Our approach enables us to state sharp qualitative results regarding uniqueness and ra- dial symmetry of solutions, as well as a characterization of nonlinearities for which the blow-up rate is universal. At last, we study in more detail the standard nonlinearities f (u) = u^p, p > 1