Boundary value problems

Friday, May 29, 2015 - 3:00pm - 3:30pm
Ariel Barton (University of Missouri)
The theory of boundary-value problems for the Laplacian in Lipschitz domains is by now very well developed. Furthermore, many of the existing tools and known results for the Laplacian have been extended to the case of second-order linear equations of the form div (A grad u), where A is a matrix of variable coefficients.
Friday, June 1, 2012 - 3:00pm - 3:30pm
Katharine Ott (University of Kentucky)
In this talk I will discuss recent results on the mixed boundary value problem in Lipschitz domains. Consider a bounded Lipschitz domain with boundary decomposed into two disjoint sets. On one portion of the boundary Neumann data is prescribed. On the remainder of the boundary Dirichlet data is prescribed. I will discuss the existence and uniqueness of solutions of the mixed problem for the Laplacian and the Lame system of elastostatics with boundary data taken from L^p, where p is greater than or equal to 1.
Tuesday, July 21, 2009 - 2:00pm - 2:50pm
David Hoff (Indiana University)
We show that, for a model system of compressible fluid flow in the upper half space of the plane, curves which intersect the boundary and across which the initial density is discontinuous become tangent to the boundary instantaneously in time. This result is closely related to the instantaneous formation of cusps in two-dimensional incompressible vortex patches.
Tuesday, March 24, 2009 - 4:30pm - 5:15pm
Linda Cummings (New Jersey Institute of Technology)
We will selectively review the application of complex variable methods to moving boundary problems, with
specific reference to the Hele-Shaw problem, and slow viscous flow driven by surface tension (in 2D, or quasi-2D).
Established theory and results will be discussed, as well as some open questions and new directions.
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