Laplace's equation

Noun

• The partial differential equation $\backslash frac\; \{\backslash partial^2\; \backslash varphi\}\{\backslash partial\; x\_1^2\}\; +\; \backslash frac\{\backslash partial^2\; \backslash varphi\}\{\backslash partial\; x\_2^2\}\; +\; \backslash cdots\; +\; \backslash frac\{\backslash partial\; ^2\; \backslash varphi\}\{\backslash partial\; x\_n^2\}\; =0$, commonly written $\backslash Delta\; \backslash varphi\; =0$ or $\backslash nabla\; ^2\backslash varphi\; =0$, where $\backslash Delta\; \backslash \; (=\; \backslash nabla^2)$ is the Laplace operator and $\backslash varphi$ is a scalar function.