Analysis Seminar

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Dirichlet Problems for Mixed Type Equations

Speaker: Kevin Payne, University of Milano

Location: Warren Weaver Hall 1302

Date: Thursday, April 20, 2017, 11 a.m.

Synopsis:

I will present some recent progress on Dirichlet problems for PDEs of mixed elliptic-hyperbolic type. This progress concerns weak well posedness, elements of spectral theory and variational characterizations. Global energy methods, developed for problems related to transonic potential flow and the possible heating in cold plasmas, will be extended to a class of geometric equations involving the Laplace-Beltrami operator for a metric of mixed Riemannian-Lorentzian signature. The results have been obtained in collaboration with Daniela Lupo, Dario Monticelli and Cathleen Morawetz.