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On Holder continuity of weak solutions to degenerate linear elliptic partial differential equations

dc.contributor.authorMombourquette, Ethan
dc.contributor.copyright-releaseNot Applicableen_US
dc.contributor.degreeMaster of Scienceen_US
dc.contributor.departmentDepartment of Mathematics & Statistics - Math Divisionen_US
dc.contributor.ethics-approvalNot Applicableen_US
dc.contributor.external-examinern/aen_US
dc.contributor.graduate-coordinatorDr. Sara Faridien_US
dc.contributor.manuscriptsNot Applicableen_US
dc.contributor.thesis-readerDr. Robert Milsonen_US
dc.contributor.thesis-readerDr. Karl Dilcheren_US
dc.contributor.thesis-supervisorDr. Scott Rodney and Dr. Keith Tayloren_US
dc.date.accessioned2013-08-21T18:03:14Z
dc.date.available2013-08-21T18:03:14Z
dc.date.defence2013-08-13
dc.date.issued2013-08-21
dc.description.abstractFor degenerate elliptic partial differential equations, it is often desirable to show that a weak solution is smooth. The first and most difficult step in this process is establishing local Hölder continuity. Sufficient conditions for establishing continuity have already been documented in [FP], [SW1], and [MRW], and their necessity in [R]. However, the complexity of the equations discussed in those works makes it difficult to understand the core structure of the arguments employed. Here, we present a harmonic-analytic method for establishing Hölder continuity of weak solutions in context of a simple linear equation div(Q?u) = f in a homogeneous space structure in order to showcase the form of the argument. Ad- ditionally, we correct an oversight in the adaptation of the John-Nirenberg inequality presented in [SW1], restricting it to a much smaller class of balls.en_US
dc.identifier.urihttp://hdl.handle.net/10222/35442
dc.language.isoenen_US
dc.subjectelliptic PDEen_US
dc.subjectpdeen_US
dc.subjectpartial differential equationsen_US
dc.subjectdegenerate sobolev spacesen_US
dc.subjectregularity of weak solutionsen_US
dc.subjectelliptic equationsen_US
dc.subjectanalysisen_US
dc.subjectharmonic analysisen_US
dc.subjectfunctional analysisen_US
dc.titleOn Holder continuity of weak solutions to degenerate linear elliptic partial differential equationsen_US

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