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Title page for ETD etd-06152015-150812


Type of Document Dissertation
Author Shao, Yuanzhen
Author's Email Address yuanzhen.shao@vanderbilt.edu
URN etd-06152015-150812
Title Theory of parabolic differential equations on singular manifolds and its applications to geometric analysis
Degree PhD
Department Mathematics
Advisory Committee
Advisor Name Title
Gieri Simonett Committee Chair
Alexander M. Powell Committee Member
Emmanuele Dibenedetto Committee Member
Larry L. Schumaker Committee Member
Zhaohua Ding Committee Member
Keywords
  • singular manifolds
  • the Yamabe flow
  • the Prous Medium equations
  • degenerate or singular parabolic equations
Date of Defense 2015-03-24
Availability unrestricted
Abstract
The main objective of this work is to establish a Holder and Lp theory for elliptic operators on manifolds with singularities. These operators may exhibit degenerate or singular behaviors while approaching the singular ends of the manifolds. Then we apply the theory established herein to several parabolic equations arising in geometric analysis, degenerate boundary value problems, and boundary blow-up problems.
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