Green's function estimates and elliptic measures for some linear elliptic equations with singular drifts.
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The purpose of this thesis is to study pointwise estimates on Green's functions and elliptic measures for linear elliptic partial differential equations that have a drift term that diverges at the boundary in several different ways. These questions are of fundamental importance in its own right in partial differential equations, with future applications in other settings such as the time-independent Schroedinger equation, as well as being important for questions of solvability of rough Dirichlet and Neumann problems for a large class of elliptic operators with singular lower order terms.
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Ph. D