EXISTENCE THEOREMS FOR A MULTIDIMENSIONAL CRYSTAL SURFACE MODEL.

In this paper we study the existence assertion of the initial boundary value problem for the equation ... This problem arises in the mathematical description of the evolution of crystal surfaces. Our investigations reveal that the exponent in the equation can have a singular part in the sense of the Lebesgue decomposition theorem, and the exponential nonlinearity somehow "cancels" it out. The net result is that we obtain a solution u that satisfies the equation and the initial boundary conditions in the almost everywhere (a.e.) sense. [ABSTRACT FROM AUTHOR]