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Results tagged with calculus-of-variations
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user 2508
Questions on the calculus of variations, which deals with the optimization of functionals mostly defined on infinite dimensional spaces.
9
votes
4
answers
1k
views
Boundedness of nonlinear continuous functionals
Let $K$ be the closed unit ball of $C[0,1]$, and let $f$ in $C(K,\mathbb{\, R})$.
Is it true that there exists an infinite dimensional reflexive subspace
$E$ of $C[0,1]$ s.t. $f(K\cap E)$ is bounded ? …
- 4,060
1
vote
Boundedness of nonlinear continuous functionals
There is a simpler counterexample for the $C[0,1]$ case. Namely,
$f(x):=$ $\log\left(1-\left\Vert x\right\Vert _{\infty}+\left\Vert Vx\right\Vert _{\infty}\right)$
,where $V$ is the classical Volter …
- 4,060