The obstacle problem for second order elliptic operators in nondivergence form

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Show simple item record Teka, Kubrom Hisho 2012-07-17T13:33:47Z 2012-07-17T13:33:47Z 2012-07-17
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. en_US
dc.language.iso en_US en_US
dc.publisher Kansas State University en
dc.subject Partial differential equations en_US
dc.subject Free boundary problems en_US
dc.subject Obstacle problem en_US
dc.title The obstacle problem for second order elliptic operators in nondivergence form en_US
dc.type Dissertation en_US Doctor of Philosophy en_US
dc.description.level Doctoral en_US
dc.description.department Department of Mathematics en_US
dc.description.advisor Ivan Blank en_US
dc.subject.umi Mathematics (0405) en_US 2012 en_US August en_US

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