Appl Math Optim 44:299–323 (2001)
2001 Springer-Verlag New York Inc.
Brittle Thin Films
and I. Fonseca
Via Beirut 4,
34014 Trieste, Italy
Department of Mathematical Sciences,
Carnegie Mellon University,
Pittsburgh, PA 15213, USA
Communicated by D. Kinderlehrer
Abstract. A two-dimensional model for brittle thin ﬁlms is obtained from a three-
dimensional fracture model for elastic material. -convergence techniques are used
to identify the limiting effective energy as the thickness of the sample approaches
Key Words. -Limit, Thin ﬁlms, Functions of bounded variation, Fracture
AMS Classiﬁcation. 35E99, 35M10, 49J45, 73C50, 73M25.
Elastic thin ﬁlms may be modeled through a limit procedure by considering three-
dimensional structures with vanishing thickness ε. In the framework of nonlinear hyper-
The research of I. Fonseca was partially supported by the National Science Foundation under Grants
Nos. DMS-9500531 and DMS-9731957, and through the Center for Nonlinear Analysis. The research of
A. Braides was partially supported by Marie-Curie Fellowship ERBFMBICT972023 of the European Union
program “Training and Mobility of Researchers.” The research of both authors was partially supported by the
Max-Planck Institute for Mathematics in the Sciences, Leipzig, Germany.