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Proceedings of the American Mathematical Society

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Boundary value estimates for harmonic forms


Authors: T. Iwaniec, M. Mitrea and C. Scott
Journal: Proc. Amer. Math. Soc. 124 (1996), 1467-1471
MSC (1991): Primary 31B25; Secondary 58G99
DOI: https://doi.org/10.1090/S0002-9939-96-03142-5
MathSciNet review: 1301031
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Abstract: We prove a bound for the $L^2$-norm of harmonic forms in terms of certain $L^p$-norms of their normal and tangential components. In turn, this is used to show the $L^2$-norm equivalence of the normal and tangential components of harmonic forms on manifolds.


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Additional Information

T. Iwaniec
Affiliation: Department of Mathematics, Syracuse University, Syracuse, New York 13244
Email: tiwaniec@mailbox.syr.edu

M. Mitrea
Affiliation: School of Mathematics, University of Minnesota, 127 Vincent Hall, 206 Church Street S.E., Minneapolis, Minnesota 55455
Email: mitrea@math.umn.edu

C. Scott
Affiliation: Department of Mathematics, University of Wisconsin, 334 Sundquist Hall, Superior, Wisconsin 54880
Email: cscott@wpo.uwsuper.edu

DOI: https://doi.org/10.1090/S0002-9939-96-03142-5
Keywords: Harmonic form, differential form, $\mathcal L^p$-norm
Received by editor(s): July 26, 1994
Received by editor(s) in revised form: October 17, 1994
Additional Notes: The first author was partially supported by NSF grant DMS 9401104
Communicated by: Albert Baernstein II
Article copyright: © Copyright 1996 American Mathematical Society