Iwaniec, T.; Mitrea, M.; Scott, C. Boundary value estimates for harmonic forms. (English) Zbl 0854.31002 Proc. Am. Math. Soc. 124, No. 5, 1467-1471 (1996). 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. Reviewer: O.-P.Piirilä (Helsinki) Cited in 4 Documents MSC: 31B25 Boundary behavior of harmonic functions in higher dimensions 31C12 Potential theory on Riemannian manifolds and other spaces Keywords:differential form; compact Riemannian maifold; harmonic form; tangential components PDFBibTeX XMLCite \textit{T. Iwaniec} et al., Proc. Am. Math. Soc. 124, No. 5, 1467--1471 (1996; Zbl 0854.31002) Full Text: DOI References: [1] J. F. Escobar, A. Freire, and M. Min-Oo, \?² vanishing theorems in positive curvature, Indiana Univ. Math. J. 42 (1993), no. 4, 1545 – 1554. · Zbl 0794.53026 · doi:10.1512/iumj.1993.42.42070 [2] T. Iwaniec, C. Scott, and B. Stroffolini, Nonlinear Potential Theory on Manifolds, (preprint) (1994). · Zbl 0963.58003 [3] B. Jawerth and M. Mitrea, Higher Dimensional Scattering Theory on \(C^1\) and Lipschitz Domains, (preprint) (1994). · Zbl 0847.35137 [4] Carlos E. Kenig, Elliptic boundary value problems on Lipschitz domains, Beijing lectures in harmonic analysis (Beijing, 1984) Ann. of Math. Stud., vol. 112, Princeton Univ. Press, Princeton, NJ, 1986, pp. 131 – 183. [5] Hermann Karcher and John C. Wood, Nonexistence results and growth properties for harmonic maps and forms, J. Reine Angew. Math. 353 (1984), 165 – 180. · Zbl 0544.58008 [6] M. Mitrea, Electromagnetic Scattering Theory on Nonsmooth Domains, (preprint) (1994). CMP 95:05 · Zbl 0829.35129 [7] Chad Scott, \?^{\?} theory of differential forms on manifolds, Trans. Amer. Math. Soc. 347 (1995), no. 6, 2075 – 2096. · Zbl 0849.58002 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.