Theory of parabolic differential equations on singular manifolds and its applications to geometric analysis

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dc.contributor.committeeChairGieri Simonett
dc.contributor.committeeMemberLarry L. Schumaker
dc.contributor.committeeMemberZhaohua Ding
dc.contributor.committeeMemberAlexander M. Powell
dc.contributor.committeeMemberEmmanuele Dibenedetto
dc.creatorShao, Yuanzhen
dc.date.accessioned2020-08-22T17:06:43Z
dc.date.available2015-12-13
dc.date.issued2015-06-16
dc.description.abstractThe 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.
dc.format.mimetypeapplication/pdf
dc.identifier.urihttps://etd.library.vanderbilt.edu/etd-06152015-150812
dc.identifier.urihttp://hdl.handle.net/1803/12584
dc.subjectsingular manifolds
dc.subjectthe Yamabe flow
dc.subjectthe Prous Medium equations
dc.subjectdegenerate or singular parabolic equations
dc.titleTheory of parabolic differential equations on singular manifolds and its applications to geometric analysis
dc.typedissertation
dc.type.materialtext
local.embargo.lift2015-12-13
local.embargo.terms2015-12-13
thesis.degree.disciplineMathematics
thesis.degree.grantorVanderbilt University
thesis.degree.leveldissertation
thesis.degree.namePHD

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