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

Journal of Mathematics and Statistics

Mohammad Al-Mahameed¹ 

关键词: Maximum principles;    elliptic partial differential equations;   

DOI  :  10.3844/jmssp.2008.9.14

学科分类：社会科学、人文和艺术（综合）

来源: Science Publications

【 摘 要 】

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.

【 授权许可】

Unknown