dc.contributor.author | Mombourquette, Ethan | |
dc.date.accessioned | 2013-08-21T18:03:14Z | |
dc.date.available | 2013-08-21T18:03:14Z | |
dc.date.issued | 2013-08-21 | |
dc.identifier.uri | http://hdl.handle.net/10222/35442 | |
dc.description.abstract | For 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.language.iso | en | en_US |
dc.subject | elliptic PDE | en_US |
dc.subject | pde | en_US |
dc.subject | partial differential equations | en_US |
dc.subject | degenerate sobolev spaces | en_US |
dc.subject | regularity of weak solutions | en_US |
dc.subject | elliptic equations | en_US |
dc.subject | analysis | en_US |
dc.subject | harmonic analysis | en_US |
dc.subject | functional analysis | en_US |
dc.title | On Holder continuity of weak solutions to degenerate linear elliptic partial differential equations | en_US |
dc.date.defence | 2013-08-13 | |
dc.contributor.department | Department of Mathematics & Statistics - Math Division | en_US |
dc.contributor.degree | Master of Science | en_US |
dc.contributor.external-examiner | n/a | en_US |
dc.contributor.graduate-coordinator | Dr. Sara Faridi | en_US |
dc.contributor.thesis-reader | Dr. Robert Milson | en_US |
dc.contributor.thesis-reader | Dr. Karl Dilcher | en_US |
dc.contributor.thesis-supervisor | Dr. Scott Rodney and Dr. Keith Taylor | en_US |
dc.contributor.ethics-approval | Not Applicable | en_US |
dc.contributor.manuscripts | Not Applicable | en_US |
dc.contributor.copyright-release | Not Applicable | en_US |