Comparison Theorems in Elliptic Partial Differential Equations with Neumann Boundary Conditions
Jeffrey J. Langford · Open Scholarship Institutional Repository (Washington University in St. Louis) · 2012
In this thesis, we study how the solution of a PDE changes when the data are rearranged. Specifically, we prove comparison theorems on spherical shells, spheres, and hemispheres, showing that under rearrangement of the data, the solution's convex mean increases. We also obtain similar weighted comparison results in balls.