# Obstacle problems with elliptic operators in divergence form

## K-REx Repository

 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, en_US 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). 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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