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Please use this identifier to cite or link to this item: http://hdl.handle.net/11299/139886

Title: On the interior regularity for degenerate elliptic equations.
Authors: Zhou, Wei
Keywords: Degenerate elliptic equations
Diffusion processes
Fully nonlinear elliptic equations
Regularity of solutions
Stochastic optimal control
Issue Date: Aug-2012
Abstract: We discuss the concept and motivations of quasiderivatives and give an example constructed by random time change, Girsanov's theorem and Levy's theorem. Then we use this probabilistic technique to investigate the regularity of the probabilistic solution of the Dirichlet problem for degenerate elliptic equations, from linear cases to fully nonlinear cases. In each Dirichlet problem we consider, the probabilistic solution is the unique solution in our setting.
Description: University of Minnesota Ph.D. dissertation. August 2012. Major: Mathematics. Advisor: Nicolai V. Krylov. 1 computer file (PDF); ii, 83 pages.
URI: http://purl.umn.edu/139886
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