Abstract
We investigate the existence and the boundary regularity of source-type self-similar solu-tions to the thin-film equation h(t) = -(h(n)h(zzz))(z) + (h(n+3))(zz),t > 0, z is an element of R; h(0, z) = omega delta(z) where n is an element of (3/2, 3), omega > 0 and 8 is the Dirac mass at the origin. It is known that the leading order expan-sion near the edge of the support coincides with that of a traveling-wave solution for the standard thin-film equation: h(t) = -(h(n)h(zzz))(z). In this paper we sharpen this result, proving that the higher-order corrections are analytic with respect to three variables: the first one is just the spatial variable, whereas the second and the third (except for n = 2) are irrational powers of it. It is known that this third variable does not appear for the thin-film equation without gravity.