Vol. 8, No. 2, 2015

Download this article
Download this article For screen
For printing
Recent Issues

Volume 17
Issue 4, 1127–1500
Issue 3, 757–1126
Issue 2, 379–756
Issue 1, 1–377

Volume 16, 10 issues

Volume 15, 8 issues

Volume 14, 8 issues

Volume 13, 8 issues

Volume 12, 8 issues

Volume 11, 8 issues

Volume 10, 8 issues

Volume 9, 8 issues

Volume 8, 8 issues

Volume 7, 8 issues

Volume 6, 8 issues

Volume 5, 5 issues

Volume 4, 5 issues

Volume 3, 4 issues

Volume 2, 3 issues

Volume 1, 3 issues

The Journal
About the journal
Ethics and policies
Peer-review process
Submission guidelines
Submission form
Editorial board
Editors' interests
ISSN: 1948-206X (e-only)
ISSN: 2157-5045 (print)
Author index
To appear
Other MSP journals
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

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 H1-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.

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
Received: 9 May 2014
Accepted: 22 January 2015
Published: 10 May 2015
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
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