# Tagged Questions

**6**

votes

**1**answer

140 views

### Generalizing “variation of parameters”

I'm stuck on generalizing an ODE formula and could use your help!
One way to think about "variation of parameters" is that it bakes the solution $z(t)=e^{At}z_0$ of $z'=Az$ (here ...

**3**

votes

**0**answers

76 views

### Variational Principle for a System of Differential Equations

I am studying a differential operator of the form $$ L\left(\begin{array}{c} u \\ v \end{array}\right) = -\Delta \left(\begin{array}{c} u \\ v \end{array}\right) + V(x)\left(\begin{array}{c} u \\ v ...

**1**

vote

**1**answer

69 views

### Implicit function theorem for boundary value problems

I have a nonlinear, two point boundary value problem of the form
$F(x, y(x), y'(x); \Omega ) = y''$ along with some boundary conditions of the form $y_\Omega(0) = a_\Omega, y_{\Omega}(1) = b_\Omega$. ...

**1**

vote

**1**answer

69 views

### variational problem related to an integral

Recently I came up with a type of variational problem in stochastic process.
It can be stated in the following way:
Given $a$ and $b$ positive, and an increasing function $f$ on $(0,1)$ (may be not ...

**4**

votes

**2**answers

390 views

### The Isoperimetric problem for domains constrained to lie between two parallel planes

It is well known that for a given volume $V$, a sphere is the shape that minimizes the surface area. I am interested in the same problem under the constraint that the shape must lie between the planes ...

**5**

votes

**1**answer

219 views

### A Lagrangian problem with a countable family of local extrema ?

Dear MO contributors,
let $r > 0, L > 0$. I am interested in maximizing the integral:
$$
\int_0^{2\pi} \frac{f(\alpha)^2 f'(\alpha)^2}{\sqrt{f(\alpha)^2 + f'(\alpha)^2}} \ \mathrm{d} \alpha
$$
...

**4**

votes

**1**answer

633 views

### Results about existence/uniqueness of solution to Euler-Lagrange equations?

While studying calculus of variations, there is one question that I feel is missing in the texts I'm reading:
What can we say about the existence and/or uniqueness of solutions to Euler-Lagrange ...

**0**

votes

**1**answer

775 views

### Functionals continuous with respect to weak convergence

It's well known that a functional of the form $u \mapsto \int f(u) dx$ is continuous with respect to weak convergence (say weak* convergence in $L^\infty$) if and only if the function $f$ is affine. ...

**7**

votes

**1**answer

373 views

### A toy model for the t-section problem

Let $S(x)$ be the area of the yellow curvilinear triangle. I'd like to find a graph for which $S(x)=H(x)$ where $H $ is some prescribed function (small, smooth, vanishing near the endpoints to any ...

**2**

votes

**5**answers

4k views

### Beginners text on Calculus of Variations

Hi,
I want to begin learning Calculus of Variations. What texts would MathOverflow recommend? Amazon shows up quite a few options:
http://tinyurl.com/36koaq4
I work on Machine Learning, and that ...

**5**

votes

**2**answers

686 views

### Is perfect play possible in continuous rock-paper-scissors? game “step size” vs. “acceleration”

The first part of my question is simple: Is every game continuous in time and strategy-space also a game of perfect information with a good equilibrium? For example, consider rock-paper-scissors. The ...