# Science at the triple point between mathematics, mechanics and materials science

## Publication 120

### Regularity In Time for Weak Solutions of a Continuum Model for Epitaxial Growth with Elasticity on Vicinal Surfaces

##### Authors:

Irene Fonseca
Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh, PA 15213

Giovanni Leoni
Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh, PA 15213

Xin Yang Lu
Department of Mathematical Sciences
Carnegie Mellon University

##### 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
15-CNA-015.pdf

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