  In this paper we prove the global existence of a strong solution to the
initial boundary value problem for the exponential partial differential
equation $\partial_tu-\Delta e^{-\Delta u}+e^{-\Delta u}-1=0$. The equation was
proposed as a continuum model for epitaxial growth of crystal surfaces on
vicinal surfaces with evaporation and deposition effects \cite{GLLM}. Our
investigations reveal that we must control the size of both $\left\| e^{-\Delta
u(x,0)}\right\|_{W^{2,2}(\Omega)}$ and $\left\| e^{\Delta
u(x,0)}\right\|_{\infty,\Omega}$ suitably to achieve our results. Related
results in \cite{GM,LS} were established via the Weiner algebra framework. Here
we offer a totally new approach, which seems to shed more light on the nature
of exponential nonlinearity.
