  We study the problem of existence and uniqueness of strong solutions to a
degenerate quasilinear parabolic non-Newtonian thin-film equation. Originating
from a non-Newtonian Navier--Stokes system the equation is derived by
lubrication theory and under the assumption that capillarity is the only
driving force. The fluid's shear-thinning rheology is described by the
so-called Ellis constitutive law. For flow behaviour exponents $\alpha \geq 2$
the corresponding initial boundary value problem fits into the abstract setting
of [4,Thm. 12.1]. Due to a lack of regularity this is not true for flow
behaviour exponents $\alpha \in (1,2)$. For this reason we prove an existence
theorem for abstract quasilinear parabolic evolution problems with H\"older
continuous dependence. This result provides existence of strong solutions to
the non-Newtonian thin-film problem in the setting of fractional Sobolev spaces
and (little) H\"older spaces. Uniqueness of strong solutions is derived by
energy methods and by using the particular structure of the equation.
