[John F Harper]
> When? It's in Hadamard's "Lectures on Cauchy's problem in linear
> partial differential equations" (written 1921 publ. 1923 Yale) with
> no indication it wasn't already well-known then.
[David Fowler]
> The latest volume, No 14, in the joint AMS/LMS series on the
> History of Mathematics is a long and fascinating account of
> Hadamard's long and fascinating life, together with a discussion
> of his work:
>
> V Maz'ya & T Shaposhnikova, Jacques Hadamard, A Universal
> Mathematician, AMS/LMS, 1998.
>
> But I can't find anything specifically on this issue in a quick
> skim through the section on PDEs.
>
I am getting a bit lost in this discussion. Anyway, Petrowki's work came
after Hadamard's book. But it discusses equations of all orders whereas
Hadamard in this book studies only second order equations.
Hadamard's first paper on PDEs appeared in 1900. The distinction between
elliptic and hyperbolic is quite clear in it and it is also clear that
he does not think it is new. What may be new is the idea that the fact
that Cauchy's problem is well posed, even for non analytic data is
characteristic of the hyperbolic case. (See Oeuvres de Jacques Hadamard,
CNRS, Paris 1968 vol 3 and, for the dates vol 4). Hadamard's works contain
a host of references which would be helpful for a historic work.
I may come back on these problems later ... if time allows me to.
Martin Zerner