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MR2299477 35R35 (35B35 35J05 47F05)
Mitrea, Irina; Ott, Katharine Counterexamples to the well-posedness of $L^p$ transmission boundary value problems for the Laplacian. Proc. Amer. Math. Soc. 135 (2007), no. 7, 2037–2043.
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