Existence of Harmonic Functions with Finite Energy on Complete Riemannian Manifolds

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Abstract

Let M be a noncompact complete Riemannian manifold. We consider the existence of harmonic functions with |∇u| ∈ L^p(M).

Keywords:

Harmonic function; finite energy; noncompact manifold
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Existence of Harmonic Functions with Finite Energy on Complete Riemannian Manifolds. (1994). Journal of Partial Differential Equations, 7(3), 257-263. https://www.global-sci.com/index.php/jpde/article/view/3776