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Publication 15-CNA-015
Irene Fonseca Giovanni Leoni Xin Yang Lu Abstract: The evolution equation derived by Xiang (SIAM J. Appl. Math.
63:241–258, 2002) to describe vicinal surfaces in heteroepitaxial growth is
$$ht = - \left[H(h_x) + (h^{-1}_2 + h_x)H_{xx}\right]_{xx}, {(1)}$$
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.Get the paper in its entirety as 15-CNA-015.pdf |