Title: Nachman's Inverse Conductivity Result

Abstract: In his 1996 paper, Nachman addressed the inverse conductivity problem in two dimensions.  If the electrical conductivity γ ∈ W^{2, p}(ℝ²)​ and is bounded below, then it is uniquely determined by its corresponding Dirichlet-to-Neumann operator Λ_γ​.  The proof of this result is constructive, involving the scattering problem for the Schrodinger equation at zero energy.  In this talk, we will give an overview of Nachman's approach.

Title:  Recovering a rough magnetic potential from boundary data

See http://www.ms.uky.edu/~hislop/PDEseminarF2015 for abstract.

TITLE:  A hybrid inverse source problem for radiative transport

ABSTRACT:  The radiative transport equation (RTE) is a model for light propagation inside a scattering medium. A classic inverse problem for the RTE is as follows.  Suppose we have an object where light propagation is modeled by the RTE, which contains a source of light. Given the ability to measure light intensity on the boundary, can we recover the light source exactly? In this talk I will give a brief introduction to the RTE and its inverse source problem, and discuss recent work on improving the stability of the problem using so-called hybrid methods. This is joint work with John Schotland and Guillaume Bal.

Title and abstract can be found at http://www.ms.uky.edu/~hislop/PDEseminarF2015 when available.

Title:  Large-Scale Boundary Regularity Estimates in Periodic Homogenization

Please see http://www.ms.uky.edu/~hislop/PDEseminarF2015 for abstract.

Please visit www.ms.uky.edu/~hislop/PDEseminarF2015 for the title and abstract and for other Analysis and PDE Seminar events.

Title:  Large-Scale Boundary Regularity Estimates in Periodic Homogenization

Abstract:  In this talk I will discuss some of recent progress on boundary regularity at large scale in homogenization of second-order elliptic systems in divergence form with rapidly oscillating periodic coecients. Here we are interested in the estimates, due to homogenization, for operators with bounded measurable coecients. These large-scale estimates, combined with the small-scale estimates obtained by rescaling, lead to the sharp regularity estimates at all scales.  In particular, the cases of the Rellich estimates in Lipschitz domains and the Lipschitz estimates in C1; domains will be presented.

TITLE: The Robin Laplacian, Faber-Krahn inequalities, and mean curvature

Abstract:  Available at http://www.ms.uky.edu/~hislop/PDEseminarS2015

Title:  Oscillatory Riemann Hilbert

Abstract:  Please see the seminar web page at http://www.ms.uky.edu/~hislop/PDEseminarS2015