On the interior regularity for degenerate elliptic equations.

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On the interior regularity for degenerate elliptic equations.

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Zhou, Wei

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2012-08

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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.

Keywords

Degenerate elliptic equations

Diffusion processes

Fully nonlinear elliptic equations

Regularity of solutions

Stochastic optimal control

Description

University of Minnesota Ph.D. dissertation. August 2012. Major: Mathematics. Advisor: Nicolai V. Krylov. 1 computer file (PDF); ii, 83 pages.

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Zhou, Wei. (2012). On the interior regularity for degenerate elliptic equations.. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/139886.

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