Obstacle problems with elliptic operators in divergence form

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dc.contributor.author Zheng, Hao en_US
dc.date.accessioned 2014-08-27T13:22:37Z
dc.date.available 2014-08-27T13:22:37Z
dc.date.issued 2014-08-27
dc.identifier.uri http://hdl.handle.net/2097/18279
dc.description.abstract Under the guidance of Dr. Ivan Blank, I study the obstacle problem with an elliptic operator in divergence form. First, I give all of the nontrivial details needed to prove a mean value theorem, which was stated by Caffarelli in the Fermi lectures in 1998. In fact, in 1963, Littman, Stampacchia, and Weinberger proved a mean value theorem for elliptic operators in divergence form with bounded measurable coefficients. The formula stated by Caffarelli is much simpler, but he did not include the proof. Second, I study the obstacle problem with an elliptic operator in divergence form. I develop all of the basic theory of existence, uniqueness, optimal regularity, and nondegeneracy of the solutions. These results allow us to begin the study of the regularity of the free boundary in the case where the coefficients are in the space of vanishing mean oscillation (VMO). en_US
dc.description.sponsorship Department of Mathematics, Kansas State Univeristy en_US
dc.language.iso en_US en_US
dc.publisher Kansas State University en
dc.subject Obstacle Problems en_US
dc.subject Elliptic en_US
dc.subject Divergence Form en_US
dc.title Obstacle problems with elliptic operators in divergence form en_US
dc.type Dissertation en_US
dc.description.degree 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
dc.date.published 2014 en_US
dc.date.graduationmonth August en_US


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