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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Non-unique solutions to boundary value problems for non-symmetric divergence form equations


Author: Andreas Axelsson
Journal: Trans. Amer. Math. Soc. 362 (2010), 661-672
MSC (2000): Primary 35J25, 42A50
Published electronically: September 18, 2009
MathSciNet review: 2551501
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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.


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Additional Information

Andreas Axelsson
Affiliation: Matematiska institutionen, Stockholms universitet, 106 91 Stockholm, Sweden
Email: andax@math.su.se

DOI: http://dx.doi.org/10.1090/S0002-9947-09-04673-X
PII: S 0002-9947(09)04673-X
Received by editor(s): September 14, 2007
Published electronically: September 18, 2009
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.