Thin elastic films: The impact of higher order perturbations

Fonseca, Irene; Francfort, Gilles; Leoni, Giovanni

doi:10.1090/S0033-569X-06-01035-7

Authors: Irene Fonseca, Gilles Francfort and Giovanni Leoni
Journal: Quart. Appl. Math. 65 (2007), 69-98
MSC (2000): Primary 49J45, 74K15
DOI: https://doi.org/10.1090/S0033-569X-06-01035-7
Published electronically: November 15, 2006
MathSciNet review: 2313149
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Abstract: The asymptotic behavior of an elastic thin film penalized by a van der Wals type interfacial energy is investigated when both its thickness and the magnitude of the additional energy vanish in the limit. Keeping track of both mid-plane and out-of-plane deformations (through the introduction of the Cosserat vector), the resulting behavior strongly depends upon the ratio between thickness and interfacial energy.

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Additional Information

Irene Fonseca
Affiliation: Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA
Email: fonseca@andrew.cmu.edu

Gilles Francfort
Affiliation: L.P.M.T.M., Université Paris-Nord, 93430 Villetaneuse, France
Email: francfor@lpmtm.univ-paris13.fr

Giovanni Leoni
Affiliation: Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, PA 15213, USA
Email: giovanni@andrew.cmu.edu

DOI: https://doi.org/10.1090/S0033-569X-06-01035-7
Received by editor(s): March 26, 2006
Published electronically: November 15, 2006
Additional Notes: The research of I. Fonseca was partially funded by the U.S. National Science Foundation DMS Grants 0103799 & 0401763, and by the Center for Nonlinear Analysis under the U.S. National Science Foundation DMS Grants 9803791 & 0405343.
This work progressed through various visits of G. Francfort to Carnegie Mellon and that author is grateful to the Center for Nonlinear Analysis for its hospitality.
The research of G. Leoni was partially funded by the U.S. National Science Foundation DMS Grant 0405423
Article copyright: © Copyright 2006 Brown University