We revisit the questions of density of smooth functions, and differential forms, in Sobolev spaces on Riemannian manifolds. We carefully show equivalence of weak covariant derivatives to weak partial derivatives.

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The Meyers–Serrin Theorem on Riemannian Manifolds: A Survey

  • Chi Hin Chan,
  • Magdalena Czubak

摘要

We revisit the questions of density of smooth functions, and differential forms, in Sobolev spaces on Riemannian manifolds. We carefully show equivalence of weak covariant derivatives to weak partial derivatives.