Transactions of the American Mathematical Society

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

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
MathSciNet review: 2551501
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Abstract | References | Similar articles | Additional information

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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