Solvability of Boundary Value Problems for Poisson’s Equation in Unbounded Domains on Noncompact Riemannian Manifolds

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A new approach is developed to posing boundary value problems on an arbitrary noncompact Riemannian manifold $$M$$. The approach is based on the introduction of classes of equivalent functions continuous on $$M $$. In particular, we establish dependence between the solvability of boundary value problems and exterior boundary value problems for some inhomogeneous linear elliptic equations on $$M$$.