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Questions on the calculus of variations, which deals with the optimization of functionals mostly defined on infinite dimensional spaces.
1
vote
Accepted
Lavrentiev phenomenon between $C^1$ + Lipschitz derivative and $C^2$
Edited.
Let $g_0^\prime(x)=|x-1/2|,\; g_0(x)=\int_0^xg_1(t)dt,\; 0\leq x\leq1$.
Then $g_0$ has continuus derivative, namely $g_0^\prime$, which is Lipschitz,
but the second derivative is discontinuous …
6
votes
Good book on Calculus of Variations
A famous (and remarkable) text is by L C Young, lectures on the calculus of variations and optimal control theory, MR0259704.
17
votes
What are the major differences between real and complex Banach space?
There are some differences. For example Bishop-Phelps theorem, which holds only in real Banach spaces. In my opinion, this qualifies as a "major theorem".
MR1749671
Lomonosov, Victor
A counterexample …