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Results tagged with calculus-of-variations
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user 25510
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 …
- 91.8k
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.
- 91.8k
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 …
- 91.8k