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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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Non-unique solutions to boundary value problems for non-symmetric divergence form equations
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by Andreas Axelsson PDF
Trans. Amer. Math. Soc. 362 (2010), 661-672 Request permission

Abstract:

We calculate explicitly solutions to the Dirichlet and Neumann boundary value problems in the upper half plane, for a family of divergence form equations having non-symmetric coefficients with a jump discontinuity. It is shown that the boundary equation method and the Lax–Milgram method for constructing solutions may give two different solutions when the coefficients are sufficiently non-symmetric.
References
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  • Auscher, P., Axelsson, A., and Hofmann, S. Functional calculus of Dirac operators and complex perturbations of Neumann and Dirichlet problems. Preprint.
  • C. Kenig, H. Koch, J. Pipher, and T. Toro, A new approach to absolute continuity of elliptic measure, with applications to non-symmetric equations, Adv. Math. 153 (2000), no. 2, 231–298. MR 1770930, DOI 10.1006/aima.1999.1899
  • Kenig, C., and Rule, D. The regularity and Neumann problem for non-symmetric elliptic operators. Preprint.
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Additional Information
  • Andreas Axelsson
  • Affiliation: Matematiska institutionen, Stockholms universitet, 106 91 Stockholm, Sweden
  • Email: andax@math.su.se
  • Received by editor(s): September 14, 2007
  • Published electronically: September 18, 2009
  • © Copyright 2009 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 362 (2010), 661-672
  • MSC (2000): Primary 35J25, 42A50
  • DOI: https://doi.org/10.1090/S0002-9947-09-04673-X
  • MathSciNet review: 2551501