Degree Name
Master of Science
Graduate Program
Mathematics
Advisor
Gluck, Mathew
Abstract
The Schauder a priori estimate for Poisson's equation is considered. These estimates are important for establishing the smoothness of solutions. Instead of proving the theorem of Schauder a priori estimate directly, this paper focuses on proving the theorem through three reductions. The first reduction normalizes the problem, the second reduction controls the H\"older semi-norm, and finally the third reduction gets a local estimate of the domain. Interpolation inequality for H\"older space and derivative estimates are used throughout this work.
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