Premium
Nondivergent elliptic equations on manifolds with nonnegative curvature
Author(s) -
Cabré Xavier
Publication year - 1997
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/(sici)1097-0312(199707)50:7<623::aid-cpa2>3.0.co;2-9
Subject(s) - mathematics , curvature , mathematical analysis , sectional curvature , pure mathematics , scalar curvature , geometry
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. © 1997 John Wiley & Sons, Inc.