The De Giorgi method : applications to degenerate PDE

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dc.contributor.advisorVasseur, Alexis F.
dc.contributor.committeeMemberCaffarelli, Luis
dc.contributor.committeeMemberPavlovic, Natasa
dc.contributor.committeeMemberSilvestre, Luis
dc.creatorStokols, Logan Frank
dc.creator.orcid0000-0002-3228-2167
dc.date.accessioned2021-05-11T00:52:35Z
dc.date.available2021-05-11T00:52:35Z
dc.date.created2020-05
dc.date.issued2020-05
dc.date.submittedMay 2020
dc.date.updated2021-05-11T00:52:36Z
dc.description.abstractThe De Giorgi method was developed in 1957 for showing continuity of non-linear elliptic problems. In this work we will apply generalizations of that method to a variety of degenerate problems. Such problems include first-order equations with negative viscosity, hypoelliptic equations including the nonlocal Focker-Planck equation, and transport-diffusion equations with boundary, for which the diffusion is of critical order and degenerates near the boundary. We will also consider a separate problem in which energy techniques can be brought to bear on a hyperbolic problem, namely the stability of shocks to conservation laws.
dc.description.departmentMathematics
dc.format.mimetypeapplication/pdf
dc.identifier.urihttps://hdl.handle.net/2152/85609
dc.identifier.urihttp://dx.doi.org/10.26153/tsw/12560
dc.language.isoen
dc.subjectPDE
dc.titleThe De Giorgi method : applications to degenerate PDE
dc.typeThesis
dc.type.materialtext
thesis.degree.departmentMathematics
thesis.degree.disciplineMathematics
thesis.degree.grantorThe University of Texas at Austin
thesis.degree.levelDoctoral
thesis.degree.nameDoctor of Philosophy

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