William Feldman, The University of Utah

Title: The pinning effect of dilute defects

We consider the Bernoulli free boundary problem with "defects", inhomogeneities in the coefficients of compact support. When the defects are small and arrayed periodically there exist plane-like solutions with a range of large-scale slopes slightly different from the background field value. This is pinning. By studying the capacity-like effect of a single defect in the Bernoulli free boundary problem we can compute the asymptotic expansion of the interval of pinned slopes as the defect size goes to zero (at least for rational normals). This is based on joint work with Inwon Kim.