dc.contributor.advisor | Hofmann, Steve, 1958- | eng |
dc.contributor.author | Le, Phi Long (Postdoctoral fellow) | eng |
dc.date.issued | 2016 | eng |
dc.date.submitted | 2016 Summer | eng |
dc.description | Abstract from public.pdf file. | eng |
dc.description | Dissertation supervisor: Dr. Steve Hoffmann. | eng |
dc.description | Includes vita. | eng |
dc.description.abstract | In this thesis, we first prove the solvability of Dirichlet problem with Lp data on the boundary for degenerate elliptic equations. Second, We obtain Lp bounds semi-groups and their gradients, and then we get Lp bounds for Riesz transform and square functions associated to a degenerate elliptic operator in divergence form. Finally, we show that for a uniformly elliptic divergence form operator defined in an open set with Ahlfors-David regular boundary, BMO- solvability implies scale invariant quantitative absolute continuity of elliptic-harmonic measure with respect to surface measure. | eng |
dc.description.bibref | Includes bibliographical references. | eng |
dc.format.extent | 1 online resource (vi, 170 pages) : illustrations | eng |
dc.identifier.merlin | b118814631 | eng |
dc.identifier.oclc | 989735740 | eng |
dc.identifier.uri | https://hdl.handle.net/10355/57234 | |
dc.identifier.uri | https://doi.org/10.32469/10355/57234 | eng |
dc.language | English | eng |
dc.publisher | University of Missouri--Columbia | eng |
dc.relation.ispartofcommunity | University of Missouri--Columbia. Graduate School. Theses and Dissertations | eng |
dc.rights | OpenAccess. | eng |
dc.rights.license | This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 License. | eng |
dc.subject.FAST | Dirichlet problem -- Numerical solutions | eng |
dc.subject.FAST | Elliptic operators | eng |
dc.title | The Dirichlet problem for elliptic and degenerate elliptic equations, and related results | eng |
dc.type | Thesis | eng |
thesis.degree.discipline | Mathematics (MU) | eng |
thesis.degree.grantor | University of Missouri--Columbia | eng |
thesis.degree.level | Doctoral | eng |
thesis.degree.name | Ph. D. | eng |