2. Classic methods

We'll restrict ourselves here to the case of N = n = 1, even though many of the results, and in particular the most important one, generalize to the higher-dimensional case. The problem is then :

where

f \in C^{2} ([a, b] \times ℝ \times ℝ)

and

I (u) = \int_{a}^{b} f (x,

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Classic methods

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Direct methods

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References

In this dossier, we have followed our book very closely (especially in the first three paragraphs). Numerous books on the subject exist, and we particularly recommend the following (precise references to works not mentioned in this bibliography can be found at ).

For classic methods: Akhiezer , Bliss , Bolza...

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