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Boundary value estimates for harmonic forms. (English) Zbl 0854.31002

Let \(M\) be an \(n\)-dimensional smooth, oriented, compact Riemannian manifold and assume that the de Rham cohomologies on \(M\) of degree \(\ell\), \(1\leq \ell\leq n-1\), and on \(\partial M\) of degree \(\ell-1\) are trivial. It is proved that for a harmonic form \(h\) of degree \(\ell\) the normal and the tangential components are \(L^2\)-equivalent.

MSC:

31B25 Boundary behavior of harmonic functions in higher dimensions
31C12 Potential theory on Riemannian manifolds and other spaces
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References:

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