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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Transmission boundary problems for Dirac operators on Lipschitz domains and applications to Maxwell’s and Helmholtz’s equations
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by Emilio Marmolejo-Olea, Irina Mitrea, Marius Mitrea and Qiang Shi PDF
Trans. Amer. Math. Soc. 364 (2012), 4369-4424 Request permission


The transmission boundary value problem for a perturbed Dirac operator on arbitrary bounded Lipschitz domains in $\mathbb {R}^3$ is formulated and solved in terms of layer potentials of Clifford-Cauchy type. As a byproduct of this analysis, an elliptization procedure for the Maxwell system is devised which allows us to show that the Maxwell and Helmholtz transmission boundary value problems are well-posed as a corollary of the unique solvability of this more general Dirac transmission problem.
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Additional Information
  • Emilio Marmolejo-Olea
  • Affiliation: Instituto de Matemáticas Unidad Cuernavaca, Universidad Nacional Autónoma de México, A.P. 273-3 Admon. 3, Cuernavaca, Morelos, 62251, México
  • Email:
  • Irina Mitrea
  • Affiliation: Department of Mathematics, Temple University, 1805 N. Broad Street, Philadelphia, Pennsylvania 19122
  • MR Author ID: 634131
  • Email:
  • Marius Mitrea
  • Affiliation: Department of Mathematics, University of Missouri, Columbia, Missouri 65211
  • MR Author ID: 341602
  • ORCID: 0000-0002-5195-5953
  • Email:
  • Qiang Shi
  • Affiliation: Department of Mathematics, Computer Science and Economics, Emporia State University, Emporia, Kansas 66801
  • Email:
  • Received by editor(s): March 13, 2010
  • Received by editor(s) in revised form: April 15, 2011
  • Published electronically: March 29, 2012
  • © Copyright 2012 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 364 (2012), 4369-4424
  • MSC (2010): Primary 30G35, 35C15, 35F15, 35J56, 42B20, 42B30, 42B37; Secondary 30E20, 31B10, 35F45, 35J25, 45B05, 65N80
  • DOI:
  • MathSciNet review: 2912458