Advances in Differential Equations

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

P. Mastrolia, D. D. Monticelli, and F. Punzo

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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

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

First available in Project Euclid: 26 October 2017

Permanent link to this document

Primary: 35J25: Boundary value problems for second-order elliptic equations 35J67: Boundary values of solutions to elliptic equations 35K10: Second-order parabolic equations 35K20: Initial-boundary value problems for second-order parabolic equations 58J05: Elliptic equations on manifolds, general theory [See also 35-XX] 58J32: Boundary value problems on manifolds 58J35: Heat and other parabolic equation methods


Mastrolia, P.; Monticelli, D. D.; Punzo, F. Elliptic and parabolic equations with Dirichlet conditions at infinity on Riemannian manifolds. Adv. Differential Equations 23 (2018), no. 1/2, 89--108.

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