Nondivergent Elliptic Equations on Manifolds with Nonnegative Curvature
نویسندگان
چکیده
Xavier Cabré Abstra t. We consider a class of second order linear elliptic operators intrinsically defined on Riemannian manifolds, and which 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.
منابع مشابه
Harnack Inequality for Nondivergent Elliptic Operators on Riemannian Manifolds
We consider second-order linear elliptic operators of nondivergence type which is intrinsically defined on Riemannian manifolds. Cabré proved a global Krylov-Safonov Harnack inequality under the assumption that the sectional curvature is nonnegative. We improve Cabré’s result and, as a consequence, we give another proof to Harnack inequality of Yau for positive harmonic functions on Riemannian ...
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