Center for                           Nonlinear Analysis CNA Home People Seminars Publications Workshops and Conferences CNA Working Groups CNA Comments Form Summer Schools Summer Undergraduate Institute PIRE Cooperation Graduate Topics Courses SIAM Chapter Seminar Positions Contact Publication 15-CNA-015 Regularity In Time for Weak Solutions of a Continuum Model for Epitaxial Growth with Elasticity on Vicinal Surfaces Irene FonsecaDepartment of Mathematical Sciences Carnegie Mellon University Pittsburgh, PA 15213fonseca@andrew.cmu.edu Giovanni LeoniDepartment of Mathematical Sciences Carnegie Mellon University Pittsburgh, PA 15213giovanni@andrew.cmu.edu Xin Yang LuDepartment of Mathematical Sciences Carnegie Mellon University Pittsburgh, PA 15213xinyang@andrew.cmu.eduAbstract: 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