Nondivergent elliptic equations on manifolds with nonnegative curvature

✍ Scribed by Xavier Cabré

• Publisher: John Wiley and Sons
• Year: 1997
• Tongue: English
• Weight: 285 KB
• Volume: 50
• Category: Article
• ISSN: 0010-3640
• DOI: 10.1002/(sici)1097-0312(199707)50:7<623::aid-cpa2>3.0.co;2-9

✦ Synopsis

We consider a class of second-order linear elliptic operators, intrinsically defined on Riemannian manifolds, that correspond to nondivergent operators in Euclidean space. Under the assumption that the sectional curvature is nonnegative, we prove a global Krylov-Safonov Harnack inequality and, as a consequence, a Liouville theorem for solutions of such equations. From the Harnack inequality, we obtain Alexandroff-Bakelman-Pucci estimates and maximum principles for subsolutions.