Vol. 8, No. 2, 2015

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Motion of three-dimensional elastic films by anisotropic surface diffusion with curvature regularization

Irene Fonseca, Nicola Fusco, Giovanni Leoni and Massimiliano Morini

Vol. 8 (2015), No. 2, 373–423
Abstract

Short time existence for a surface diffusion evolution equation with curvature regularization is proved in the context of epitaxially strained three-dimensional films. This is achieved by implementing a minimizing movement scheme, which is hinged on the ${H}^{-1}$-gradient flow structure underpinning the evolution law. Long-time behavior and Liapunov stability in the case of initial data close to a flat configuration are also addressed.

Keywords
minimizing movements, surface diffusion, gradient flows, higher order geometric flows, elastically stressed epitaxial films, volume-preserving evolution, long-time behavior, Liapunov stability
Mathematical Subject Classification 2010
Primary: 35K25, 53C44, 74K35, 35Q74
Secondary: 37B25
Milestones
Accepted: 22 January 2015
Published: 10 May 2015
Authors
 Irene Fonseca Department of Mathematical Sciences Carnegie Mellon University Pittsburgh, PA 15213 United States Nicola Fusco Dipartimento di Matematica e Applicazioni “R. Caccioppoli” Università degli Studi di Napoli “Federico II” I-80126 Napoli Italy Giovanni Leoni Department of Mathematical Sciences Carnegie Mellon University Pittsburgh, PA 15213 United States Massimiliano Morini Dipartimento di Matematica Università degli Studi di Parma I-43121 Parma Italy