Christopher Larsen, Department of Mathematics, Worcester Polytechnic Institute.
"Avoiding the Neumann sieve in a problem of fracture growth"
In proving existence for mathematical models of brittle fracture growth, the following problem arrises:
subject to on , where . If (in the sense of SBV compactness), does the corresponding minimality hold for ?
The problem of the "Neumann sieve" suggests that this minimality may be false, though Dal Maso and Toader found a way around it, assuming that the number of components of is bounded and that . It turns out that there is a way to completely avoid the issue of the Neumann sieve, which I will describe in this talk. This is part of joint work with G. Francfort.
Location: PPB 300