Dirichlet energy

Etymology
Named after German mathematician (1805-1859), who made significant contributions to the theory of Fourier series.

Noun

 * 1)  A quadratic functional which, given a real function defined on an open subset of ℝn, yields a real number that is a measure of how variable said function is.

Usage notes

 * In mathematical terms, given an open set $$\Omega\subseteq\R^n$$ and a function $$u:\Omega\to\R$$, the Dirichlet energy of $$u$$ is $$\textstyle E[u] = \frac 1 2 \int_\Omega \| \nabla u(x) \|^2 \, dx$$, where $$\nabla u: \Omega\to\R^n$$ denotes the gradient vector field of $$u$$.

Translations

 * Dutch: Dirichlet-energie
 * Italian: energia di Dirichlet
 * Spanish: energía de Dirichlet