Abstract

This paper deals with some mathematical models arising in the theory of epitaxial growth of crystal. We focalize the study on a stationary problem which presents some analytical difficulties. We study the existence of solutions. The central model in this work is given by the following fourth order elliptic equation,Δ2u=det(D2u)+λf,x∈Ω⊂R2,conditions on ∂Ω. The framework to study the problem deeply depends on the boundary conditions.

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