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In this article we prove the global existence of a unique strong solution tothe initial boundary-value problem for a fourth-order exponential PDE. Theequation we study was originally proposed to study the evolution of crystalsurfaces, and was derived by applying a nonstandard scaling regime to amicroscopic Markov jump process with Metropolis rates. Our investigation herefinds that compared to the PDE's which use Arhenious rates, (and also have afourth order exponential nonlinearity) the hyperbolic sine nonlinearity in ourequation can offer much better control over the exponent term even in highdimensions.

Existence Theorems for a Fourth-Order Exponential PDE Related to Crystal Surface Growth