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This paper provides solutions to second order boundary value problems for differential forms by means of the method applied in [3] for first order problems. These  r -forms  f  ∈  C  2,λ (Ω¯) have prescribed conditions Δ f , where Ω is a subset of a compact Riemannian manifold and ∂Ω ≠ Ø;. Further constraints are imposed by the boundary conditions and topological properties. Such boundary value problems play a prominent role in the proof of the Hodge–Kodaira–Morrey decomposition of  L  2 , as demonstrated in [9]. Our approach, based on the boundary integral method, will provide additional results, which will be essential parts of a direct proof of the corresponding Banach space decompositions of  L   p  .

Boundary value problems for differential forms on compact Riemannian manifolds, Part II