Elliptic and parabolic equations with Dirichlet conditions at infinity on Riemannian manifolds

الأصل · EN

We investigate existence and uniqueness of bounded solutions of parabolic equations with unbounded coefficients in M× R+, where M is a complete noncompact Riemannian manifold. Under specific assumptions, we establish existence of solutions satisfying prescribed conditions at infinity, depending on the direction along which infinity is approached. Moreover, the large-time behavior of such solutions is studied. We consider also elliptic equations on M with similar conditions at infinity.