Abstract
The main goal here is to develop a Calderón-Zygmund theory for singular integral operators of boundary layer potential type naturally associated with second-order elliptic systems on Riemannian manifolds which is effective in the treatment of boundary value problems in rough domains.
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References
D.S. Jerison and C.E. Kenig, Boundary behavior of harmonic functions in nontangentially accessible domains, Adv. in Math., 46 (1982), no. 1, 80–147.
M. Mitrea and M. Taylor, Boundary layer methods for Lipschitz domains in Riemannian manifolds, Journal of Functional Analysis 163, 181–251 (1999).
D. Mitrea, M. Mitrea, and M. Taylor, Layer Potentials, the Hodge Laplacian, and Global Boundary Problems in Nonsmooth Riemannian Manifolds, Memoirs of the American Mathematical Society, March 2001, Volume 150, Number 713.
S. Hofmann, M. Mitrea, and M. Taylor, Singular Integrals and Elliptic Boundary Problems on Regular Semmes–Kenig–Toro Domains, International Mathematics Research Notices, Vol. 2010, No. 14, pp. 2567–2865.
D. Mitrea, Irina Mitrea, M. Mitrea, and M. Taylor, Boundary Problems for the Hodge–Laplacian on Regular Semmes–Kenig–Toro Subdomains of Riemannian Manifolds, book manuscript, 2014.
Acknowledgements
The first-named author was partially supported by the Simons Foundation grant # 200750. The second-named author was partially supported by the Simons Foundation grant # 318658; part of this work has been carried out while she was a von Neumann Fellow at the Institute for Advanced Study at Princeton, with partial support from Temple University. The third-named author was partially supported by the Simons Foundation grant # 281566, and a University of Missouri Research Leave.
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Mitrea, D., Mitrea, I., Mitrea, M., Schmutzler, B. (2015). Calderón–Zygmund Theory for Second-Order Elliptic Systems on Riemannian Manifolds. In: Constanda, C., Kirsch, A. (eds) Integral Methods in Science and Engineering. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-16727-5_35
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DOI: https://doi.org/10.1007/978-3-319-16727-5_35
Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-319-16726-8
Online ISBN: 978-3-319-16727-5
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