- #1

- 27

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**Appoximate a non-analytic function?**

Dear all,

is there a way to do that near a point?

Also, for a given ODE or even PDE, is there a criterion to show whether its solution is analytic? Is it a proper question in fact?

Thanks!

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- Thread starter zeebek
- Start date

- #1

- 27

- 0

Dear all,

is there a way to do that near a point?

Also, for a given ODE or even PDE, is there a criterion to show whether its solution is analytic? Is it a proper question in fact?

Thanks!

Last edited:

- #2

- 34

- 0

Regarding the DE/PDE's here's a starting point for you:

http://en.wikipedia.org/wiki/Picard–Lindelöf_theorem

If you ever find a way to do it in general for PDE's, you're a genius.

- #3

- 27

- 0

"Are the solutions of regular problems in the calculus of variations always analytic?"

Here is an overview http://math.univ-lyon1.fr/~clarke/Clarke_Regularity.pdf

The first question: for a certain type of functions Taylor series do not work at some points even though they are infitely differentiable there like this one

http://planetmath.org/?op=getobj&from=objects&id=3081

So the question is is there a method to approximate such a function near a point still.

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