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Energy-minimizing set of discrete points in a bounded domain
Let $\Omega \subset \mathbb{R}^3$ be a smooth, bounded domain.
Let $x_1,\ldots,x_n \in \overline{\Omega}$ be chosen so as to minimize
$$
\sum_{1\leq i<j\leq n} \frac{1}{|y_i - y_j|}
$$
over all ...
5
votes
2
answers
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Most general conditions for (weak or classical) solutions to Poisson's equation
I thought I knew this but have found it surprisingly difficult to find good references. I am interested in solving
$$
\left\{
\begin{align}
& \Delta \psi = - \rho & & \mbox{in } \mathbb{...