Boundary value estimates for harmonic forms
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- by T. Iwaniec, M. Mitrea and C. Scott PDF
- Proc. Amer. Math. Soc. 124 (1996), 1467-1471 Request permission
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.References
- J. F. Escobar, A. Freire, and M. Min-Oo, $L^2$ vanishing theorems in positive curvature, Indiana Univ. Math. J. 42 (1993), no. 4, 1545–1554. MR 1266105, DOI 10.1512/iumj.1993.42.42070
- T. Iwaniec, C. Scott, and B. Stroffolini, Nonlinear Potential Theory on Manifolds, (preprint) (1994).
- B. Jawerth and M. Mitrea, Higher Dimensional Scattering Theory on $C^1$ and Lipschitz Domains, (preprint) (1994).
- 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. MR 864372
- Hermann Karcher and John C. Wood, Nonexistence results and growth properties for harmonic maps and forms, J. Reine Angew. Math. 353 (1984), 165–180. MR 765831
- M. Mitrea, Electromagnetic Scattering Theory on Nonsmooth Domains, (preprint) (1994).
- Chad Scott, $L^p$ theory of differential forms on manifolds, Trans. Amer. Math. Soc. 347 (1995), no. 6, 2075–2096. MR 1297538, DOI 10.1090/S0002-9947-1995-1297538-7
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
- MR Author ID: 341602
- ORCID: 0000-0002-5195-5953
- 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
- 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
- © Copyright 1996 American Mathematical Society
- 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