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Summary: Acerbi, Fonseca and Fusco 1
REGULARITY RESULTS FOR EQUILIBRIA
IN A VARIATIONAL MODEL FOR FRACTURE
Emilio Acerbi 1
Irene Fonseca 2
Nicola Fusco 3
Abstract
In recent years models describing interactions between fracture and damage have been
proposed in which the relaxed energy of the material is given by a functional involving bulk
and interfacial terms, of the form
G(K, u) :=
\K
F (u) dx +
\K
|u - g|q
dx + HN-1
(K ) ,
where is an open, bounded subset of RN , q 1, g L(; RN ), , > 0, the bulk energy
density F is quasiconvex, K RN is closed, and the admissible deformation u : RN
is C1 in \ K. One of the main issues has to do with regularity properties of the "crack
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