CMU Campus
Center for                           Nonlinear Analysis
CNA Home People Seminars Publications Workshops and Conferences CNA Working Groups CNA Comments Form Summer Schools Summer Undergraduate Institute PIRE Cooperation Graduate Topics Courses SIAM Chapter Seminar Positions Contact
Seminar Abstracts

Ana Soane, University of Maryland, Baltimore County

Variational problems in weighted Sobolev spaces on non-smooth domains

Abstract

We study the Poisson problem -Δ u = f and Helmholtz problem -Δ u + λ u = f in bounded domains with angular corners in the plane and u=0 on the boundary. On non-convex domains of this type, the solutions are in the Sobolev space H1 but not in H2 even though f may be very regular. We formulate these as variational problems in weighted Sobolev spaces and prove existence and uniqueness of solutions in what would be weighted counterparts of H2 ∩ H10. The specific forms of our variational formulations are motivated by, and applied to, a finite element scheme for the time-dependent Navier-Stokes equations.

TUESDAY, January 22, 2008
Time: 1:30 P.M.
Location: PPB 300