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Article: Maximum principles for second order elliptic equations in nondivergence form and applications.(Report)
- Article from:
- Journal of Mathematics and Statistics
- Article date:
- January 1, 2008
- Author:
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Abstract: The main objectives of this study were to introduce a maximum principle for second order elliptic equations in nondivergence form and to use a nondivergence technique called the ABP method to establish the maximum principles in small domains. The advantage of this work was that we obtain a maximum principle for equations with discontinuous coefficients of the leading terms and the ABP estimate was a bound for solutions of uniformly elliptic equations written in nondivergence form with measurable coefficients. It was an essential tool in the regularity theory for fully nonlinear equations.
Key words: Maximum principles, elliptic partial differential ...