Search Results
| Search type | Search syntax |
|---|---|
| Tags | [tag] |
| Exact | "words here" |
| Author |
user:1234 user:me (yours) |
| Score |
score:3 (3+) score:0 (none) |
| Answers |
answers:3 (3+) answers:0 (none) isaccepted:yes hasaccepted:no inquestion:1234 |
| Views | views:250 |
| Code | code:"if (foo != bar)" |
| Sections |
title:apples body:"apples oranges" |
| URL | url:"*.example.com" |
| Saves | in:saves |
| Status |
closed:yes duplicate:no migrated:no wiki:no |
| Types |
is:question is:answer |
| Exclude |
-[tag] -apples |
| For more details on advanced search visit our help page | |
Results tagged with calculus-of-variations
Search options answers only
not deleted
user 6101
Questions on the calculus of variations, which deals with the optimization of functionals mostly defined on infinite dimensional spaces.
11
votes
Accepted
Functional minimization problem
Actually this is one of the oldest problems in the calculus of variations. It's named "the Newton problem" after Sir Isaac Newton, who studied it in 1685. It arises from the determination of the optim …
- 55.5k
3
votes
Accepted
Critical points in Hilbert space
Especially in Calculus of Variations and Mechanics, a submanifold $Y$ of a manifold $X$ is usually called "a natural constraint" for a functional $f$ on $X$, if the special circumstance that you are c …
- 55.5k
2
votes
Approximating functions in $H_0^1(\Omega)$ by piecewise affine ones.
Certainly, a piecewise affine function $f$ (meaning, a function which is affine on each open simplex of some triangulation of the domain) is in $W^{1,\\ p}_{loc}$ for some $1\leq p\leq \infty$ if and …
- 55.5k
1
vote
optimize with respect to domain shape
I'd say these belongs to the family of shape optimization problems in the Calculus of Variations (of whom the most famous example is the isoperimetric problem). As to the first one, you should make s …
- 55.5k
3
votes
Accepted
Is vesica piscis a maximal length curve constrained to two points?
The length of these curves is unbounded. For a positive integer $n$ consider a triangular wave
$f_n:[0,1]\to\mathbb{R}$ with support on $[1/3,2/3]$, making $n$ (isosceles) triangular impulses on $[1 …
- 55.5k
1
vote
Accepted
Converting an integral equation into a differential equation
This is elementary but let's state it. First one only considers smooth test functions $h$ with compact support (so that the last two terms disappear). If $F(x):=\int_0^xf(t)dt$, integrating by parts t …
3
votes
Minimizing sequence $\implies$ Palais–Smale sequence
In fact it's just the MVT to $DF$:
$$\|DF(x_n)-DF(y_n)\|\le \|x_n-y_n\|\sup\|D^2F\|=O(\|x_n-y_n\|)=o(1),$$ so $\|DF(x_n)\|=o(1)$ too.
$$*$$
Note that if $D^2f$ is not bounded, it is not true, and (a …
- 55.5k
3
votes
Choquet theory and Hilbert's fourth problem
It seems to me that the set of projective semi-distances that you describe in the example (let's call them of type I) can be slightly generalized the following way. In the definition of $d_H$, let $H …
- 55.5k