Counterexamples to the well-posedness of $L^p$ transmission boundary value problems for the Laplacian
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- by Irina Mitrea and Katharine Ott PDF
- Proc. Amer. Math. Soc. 135 (2007), 2037-2043 Request permission
Abstract:
In this note we show that the well-posedness range $p\in (1,2]$ for $L^p$ transmission boundary value problems for the Laplacian in the class of Lipschitz domains established by Escauriaza and Mitrea (2004) is sharp. Our approach relies on Mellin transform techniques for singular integrals naturally associated with the transmission problems and on a careful analysis of the $L^p$ spectra of such singular integrals.References
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Additional Information
- Irina Mitrea
- Affiliation: Department of Mathematics, University of Virginia, Charlottesville, Virginia 22904
- MR Author ID: 634131
- Email: im3p@virginia.edu
- Katharine Ott
- Affiliation: Department of Mathematics, University of Virginia, Charlottesville, Virginia 22904
- MR Author ID: 810101
- Email: kott@virginia.edu
- Received by editor(s): January 22, 2006
- Published electronically: February 28, 2007
- Additional Notes: The first author was supported in part by NSF Grant DMS 0547944 and a University of Virginia FEST Grant.
The second author was supported in part by an Aerospace Graduate Research Fellowship - Communicated by: Michael T. Lacey
- © Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 135 (2007), 2037-2043
- MSC (2000): Primary 45E05, 47A05; Secondary 35J25, 42B20
- DOI: https://doi.org/10.1090/S0002-9939-07-08686-8
- MathSciNet review: 2299477