Journal of Mathematics and Statistics

Maximum Principles for Second Order Elliptic Equations in Nondivergence Form and Applications

Mohammad Al-Mahameed

DOI : 10.3844/jmssp.2008.9.14

Journal of Mathematics and Statistics

Volume 4, Issue 1

Pages 9-14

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.

Copyright

© 2008 Mohammad Al-Mahameed. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.