TY  - JOUR
AU  - Al-Mahameed, Mohammad 
PY  - 2008
TI  - Maximum Principles for Second Order Elliptic Equations in Nondivergence Form and Applications
JF  - Journal of Mathematics and Statistics
VL  - 4
IS  - 1
DO  - 10.3844/jmssp.2008.9.14
UR  - https://thescipub.com/abstract/jmssp.2008.9.14
AB  - 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.