[FOM] Hadamard's principle

Bas Spitters spitters at cs.ru.nl
Thu Feb 10 03:34:14 EST 2005

On Thursday 10 February 2005 03:05, Jeffery Zucker wrote:
> I would like to refer, at least briefly,
> to what is known as "Hadamard's principle".

Here is what Micheal Beeson (Foundations of constructive mathematics, p368) 
writes about this:
Recognition of this idea goes back at least to Hadamard, who formulated three 
conditions for a problem in differential equations to be "well-posed" (see 
e.g. Courant-Hilbert [1953], p.227):
(i) existence of the solution
(ii) uniqueness of the solution
(iii) continuous dependence of the solution on the parameters (initital 
conditions or boundary conditions, for example). 
Hadamard's formulation makes it seem that his motivation for the condition 
(iii) was that he really wanted to require the solution to be *computable*, 
but did not know a way to state this precisely...
(emphasis by Beeson)

Beeson uses this as an introduction to the tight connections between 
constructivity and continuity. He refers to Hadamard[1952] p38 for the 
orginal quote, which dates from 1923.

Hadamard[1952] Lectures on Cauchy's Problem in linear Partial Differential 
Equations, Dover, 1952.


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