The obstacle problem for second order elliptic operators in nondivergence form
| dc.contributor.author | Teka, Kubrom Hisho | |
| dc.date.accessioned | 2012-07-17T13:33:47Z | |
| dc.date.available | 2012-07-17T13:33:47Z | |
| dc.date.graduationmonth | August | |
| dc.date.issued | 2012-07-17 | |
| dc.date.published | 2012 | |
| dc.description.abstract | We study the obstacle problem with an elliptic operator in nondivergence form with principal coefficients in VMO. We develop all of the basic theory of existence, uniqueness, optimal regularity, and nondegeneracy of the solutions. These results, in turn, allow us to begin the study of the regularity of the free boundary, and we show existence of blowup limits, a basic measure stability result, and a measure-theoretic version of the Caffarelli alternative proven in Caffarelli's 1977 paper ``The regularity of free boundaries in higher dimensions." Finally, we show that blowup limits are in general not unique at free boundary points. | |
| dc.description.advisor | Ivan Blank | |
| dc.description.degree | Doctor of Philosophy | |
| dc.description.department | Department of Mathematics | |
| dc.description.level | Doctoral | |
| dc.identifier.uri | http://hdl.handle.net/2097/14035 | |
| dc.language.iso | en_US | |
| dc.publisher | Kansas State University | |
| dc.rights | © the author. This Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s). | |
| dc.rights.uri | http://rightsstatements.org/vocab/InC/1.0/ | |
| dc.subject | Partial differential equations | |
| dc.subject | Free boundary problems | |
| dc.subject | Obstacle problem | |
| dc.subject.umi | Mathematics (0405) | |
| dc.title | The obstacle problem for second order elliptic operators in nondivergence form | |
| dc.type | Dissertation |
