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These notes provide a self-contained introduction to Schauder theory onmanifolds. First, we derive Schauder estimates for a fourth-order paraboliclinear problem with a first- and third-order boundary condition on a smoothcompact manifold M. Then, applying these, we prove the existence of solutionsand study the associated elliptic problem.

Parabolic and Elliptic Schauder Theory on Manifolds for a Fourth-Order Problem with a First- and a Third-Order Boundary Condition