Comparison Theorems in Elliptic Partial Differential Equations with Neumann Boundary Conditions
Date of Award
Doctor of Philosophy (PhD)
Chair and Committee
Albert Baernstein II
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.
Langford, Jeffrey, "Comparison Theorems in Elliptic Partial Differential Equations with Neumann Boundary Conditions" (2012). All Theses and Dissertations (ETDs). 706.
Permanent URL: http://dx.doi.org/10.7936/K7R20ZGM