Dirichlet's principle

In mathematics, and particularly in potential theory, Dirichlet's principle is the assumption that the minimizer of a certain energy functional is a solution to Poisson's equation.

Dirichlet's principle states that, if the function ${\displaystyle u(x)}$ is the solution to Poisson's equation

on a domain ${\displaystyle \Omega }$ of ${\displaystyle \mathbb {R} ^{n}}$ with boundary condition

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