Advances in Differential Equations

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

Abstract

We investigate existence and uniqueness of bounded solutions of parabolic equations with unbounded coefficients in $M\times \mathbb R_+$, 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. We consider also elliptic equations on $M$ with similar conditions at infinity.

Article information

Source
Adv. Differential Equations Volume 23, Number 1/2 (2018), 89-108.

Dates
First available in Project Euclid: 26 October 2017

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