= Solution
\b[The <Cauchy-Kovalevskaya theorem> cannot be applied to merely $C^2$, non-$C^3$ <Cauchy data>.] It requires <real analytic> data.
There is also no $C^2$ solution of the <Laplace equation> on a neighborhood of a point where one of these prescribed traces fails to be $C^3$. By interior <elliptic regularity>, any such solution would be <smooth> and <real analytic>. On the <real analytic> hypersurface retained from the preceding part, both its restriction and its <normal derivative> would then be <real analytic>, hence $C^3$. This contradicts the prescribed trace. \b[There is no solution on a neighborhood of all of $\Gamma$ with the stated non-$C^3$ data.] This does not exclude solutions near other points where the data happen to be <real analytic>.
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