A new approach to irreversible quasistatic fracture growth is given, by means of Young measures. The study concerns a cohesive zone model with prescribed crack path, when the material gives different responses to loading and unloading phases. In the particular situation of constant unloading response, the result contained in [G. Dal Maso and C. Zanini, 137 (2007) 253–279] is recovered. In this case, the convergence of the discrete time approximations is improved.

A new approach to irreversible quasistatic fracture growth
is given, by means of Young measures.
The study concerns a cohesive zone model
with prescribed crack path, when the material gives
different responses to loading and unloading phases.
In the particular situation of constant unloading response,
the result contained in [G. Dal Maso and C. Zanini,
(2007) 253–279] is recovered.
In this case, the convergence of the discrete time approximations
is improved.

The isoperimetric inequality for Steiner symmetrization of any codimension is investigated and the equality cases are characterized. Moreover, a quantitative version of this inequality is proven for convex sets.

The adjoint method, recently introduced by Evans, is used to study obstacle problems, weakly coupled systems, cell problems for weakly coupled systems of Hamilton − Jacobi equations, and weakly coupled systems of obstacle type. In particular, new results about the speed of convergence of some approximation procedures are derived.

Download Results (CSV)