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The obstacle problem for second order elliptic operators in nondivergence form

Doctor of Philosophy / Department of Mathematics / Ivan Blank / 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.

Identiferoai:union.ndltd.org:KSU/oai:krex.k-state.edu:2097/14035
Date January 1900
CreatorsTeka, Kubrom Hisho
PublisherKansas State University
Source SetsK-State Research Exchange
Languageen_US
Detected LanguageEnglish
TypeDissertation

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