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arXiv · 1511.09023

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

Paolo Mastrolia·Dario D. Monticelli·Fabio Punzo
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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. Moreover, the large-time behavior of such solutions is studied. We consider also elliptic equations on $M$ with similar conditions at infinity.

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Paolo Mastrolia, Dario D. Monticelli, Fabio Punzo. 2015-11-29. Elliptic and parabolic equations with Dirichlet conditions at infinity on Riemannian manifolds. https://arxiv.org/abs/1511.09023

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