# Tagged Questions

**1**

vote

**1**answer

233 views

### A 'conjecture' on critical elliptic pde

I conjecture the following.
Let $\Omega=\mathbb{R}^3-\overline{B_1(0)}$. Define
$$E_{\Omega}(u)=\frac{1}{2}\int_{\Omega}|\nabla u|^2dx-\frac{1}{6}\int_{\Omega}|u|^6dx.$$
$E_{\mathbb{R}^3}$ is defined ...

**2**

votes

**0**answers

218 views

### Periodic orbits of Hamiltonian systems

Consider a second order Hamiltonian system of the type
$$
\ddot{x}+V'(x)=0, \quad x \in \mathbb{R}^N.
$$
Under very `natural assumptions' it is possible to prove the existence of a non constant ...

**12**

votes

**1**answer

682 views

### What braking strategy is most fuel-efficient?

You notice a stop-light ahead of you and it is currently red. You can't run the red light, so you will have to brake, but braking wastes energy and you want to be as fuel efficient as possible. What ...

**4**

votes

**2**answers

943 views

### Minimizing a function containing an integral

I am trying to optimize a function of the following form:
$L = \int_{t=0}^{T}(AR-x)dt$, where A is a system parameter
i.e. I am trying to find the optimum x(t) that minimizes L over all admissible ...