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Oblique and normal transmission problems for Dirac operators with strongly Lipschitz interfaces
Australian Natl Univ, Inst Math Sci, Ctr Math and Applicat, Canberra, ACT, Australia.
2003 (English)In: Communications in Partial Differential Equations, ISSN 0360-5302, E-ISSN 1532-4133, Vol. 28, no 11-Dec, 1911-1941 p.Article in journal (Refereed) Published
Abstract [en]

We investigate transmission problems with strongly Lipschitz interfaces for the Dirac equation by establishing spectral estimates on an associated boundary singular integral operator, the rotation operator. Using Rellich estimates we obtain angular spectral estimates on both the essential and full spectrum for general bi-oblique transmission problems. Specializing to the normal transmission problem, we investigate transmission problems for Maxwells equations using a nilpotent exterior/interior derivative operator. The fundamental commutation properties for this operator with the two basic reflection operators are proved. We show how the L-2 spectral estimates are inherited for the domain of the exterior/interior derivative operator and prove some complementary eigenvalue estimates. Finally we use a general algebraic theorem to prove a regularity property needed for Maxwells equations.

Place, publisher, year, edition, pages
2003. Vol. 28, no 11-Dec, 1911-1941 p.
National Category
Medical and Health Sciences
URN: urn:nbn:se:liu:diva-53542DOI: 10.1081/PDE-120025490OAI: diva2:289449
Available from: 2010-01-25 Created: 2010-01-25 Last updated: 2012-01-03Bibliographically approved

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Axelsson Rosén, Andreas
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Communications in Partial Differential Equations
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