|GEOMETRIC PDE SEMINAR|
|Topic:||The Composite Membrane Problem|
|Affiliation:||Rutgers University and Member, School of Mathematics|
|Date:||Thursday, December 4|
|Time/Room:||1:30pm - 3:30pm/S-101|
We address the problem of building a body of specified shape and of specified mass, out of materials of varying density so as to minimize the first Dirichlet eigenvalue. It leads to a free boundary problem and many uniqueness questions, The regularity of the free boundary and optimal regularity of the solution then depends on blow-up analysis and a monotonicity formula. Full regularity of the free boundary so far has only been achieved in dimension two where the tangent cones obtained via blow-up are seen to be unstable. This is in part joint work with C. Kenig and Tung To.