Thesis Defense - Comparison Theorems in Elliptic Partial Differential Equations with Neumann Boundary Conditions

Jeffrey Langford, Department of Mathematics, Washington University in St. Louis

April 13, 2012 - 8:00 am to 10:00 am
Location: Cupples I, Room 199 | Hosts: Profs. Al Baerstein (Washington University in St. Louis) & Richard Laugesen (University of Urbana, Illinois)

Abstract: For a partial differential equation (PDE) with Neumann boundary conditions, we ask how the input data should be arranged so that the solution has maximal L^p norms and oscillation. We begin our discussion with a physically motivated (open) problem and proceed to discuss the history of comparison theorems in PDEs with Dirichlet boundary conditions. We continue by discussing my comparison results that impose Neumann boundary conditions, and use these results to arrive at a conjecture to the original physically motivated problem.

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