Vol. 8, No. 2, 2015

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

Volume 16
Issue 2, 309–612
Issue 1, 1–308

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
Editorial Board
Editors’ Interests
Subscriptions
 
Submission Guidelines
Submission Form
Policies for Authors
Ethics Statement
 
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
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 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.

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
Received: 9 May 2014
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