Transactions of the American Mathematical Society

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

Author(s): Andreas Axelsson
Journal: Trans. Amer. Math. Soc. 362 (2010), 661-672.
MSC (2000): Primary 35J25, 42A50
Posted: September 18, 2009
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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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Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 35J25, 42A50

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

DOI: 10.1090/S0002-9947-09-04673-X
PII: S 0002-9947(09)04673-X
Received by editor(s): September 14, 2007
Posted: September 18, 2009
Copyright of article: Copyright 2009, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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ISSN 1088-6850(e) ISSN 0002-9947(p)

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