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

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 Added by Dario Monticelli
 Publication date 2015
  fields
and research's language is English




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We investigate existence and uniqueness of bounded solutions of parabolic equations with unbounded coefficients in $Mtimes mathbb R_+$, 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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