Summary
A Dirichlet problem for an equation of mixed type with a discontinuous coefficient is considered for a rectangle. In one part of the rectangle, Laplace's equation is specified while the wave equation is specified in the other part. The questions of existence, non-existence, uniqueness and non-uniqueness are discussed.
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References
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Cannon, J.R. A dirichlet problem for an equation of mixed type with a discontinuous coefficient. Annali di Matematica 61, 371–377 (1963). https://doi.org/10.1007/BF02410656
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DOI: https://doi.org/10.1007/BF02410656