Date of Original Version
This is the accepted version of the article which has been published in final form at http://dx.doi.org/10.1080/03605302.2015.1045074
Abstract or Description
The evolution equation derived by Xiang (SIAM J. Appl. Math. 63:241–258, 2002) to describe vicinal surfaces in heteroepitaxial growth is
ht = − [H(hx) + (hx −1 + hx )hxx ]xx , (1)
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.
Communications in Partial Differential Equations, 40, 10, 1942-1957.