Elliptic partial differential equations on the warped products of riemannian manifolds

Abstract

The properties of bounded solutions of elliptic partial differential equations are studied on the Riemannian manifolds of a certain type. The exact condition of solvability of the Dirichlet problem at infinity is proved. Also the condition of existence of the limit at infinity of bounded solutions and the condition of validity of the Liouville theorem are found.

Keywords:

• Elliptic partial differential equations
• Riemannian manifolds
• the Dirichlet problem
• the Liouville theorem