Published Paper

Inserted: 8 sep 2015
Last Updated: 8 sep 2015

Journal: Commun. Part. Diff. Eq.
Volume: 40
Number: 10
Pages: 1942-1957
Year: 2015

Abstract:

The evolution equation derived by Xiang (SIAM J. Appl. Math. 63:241-258, 2002) to describe vicinal surfaces in heteroepitaxial growth is $h_t=-[ H(h_x)+(h_x^{-1}+h_x ) h_{xx} ]_{xx} $, where $h$ denotes the surface height of the film, and $H$ is the Hilbert transform. Existence of solutions was} obtained by Dal Maso, Fonseca and Leoni (Arch. Rational Mech. Anal. 212: 1037--1064, 2014). The regularity in time was left unresolved. The aim of this paper is to prove existence, uniqueness, and Lipschitz regularity in time for weak solutions, under suitable assumptions on the initial datum.

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