  Taking into account the occurrence of a zero of the surface diffusion current
and the requirement of the Ehrlich-Schwoebel effect, Siegert et al
\cite{Siegert94} formulate a model of Langevin type that describes the growth
of pyramidlike structures on a surface under conditions of molecular beam
epitaxy, and that the slope of these pyramids is selected by the crystalline
symmetries of the growing film. In this article, the existence and uniqueness
of weak solution to an initial boundary value problem for this model is proved,
in the case that the noise is neglected. The regularity of the weak solution to
models, with/without slope selection, is also investigated.
