Dirichlet boundary condition

Summary

A Dirichlet boundary condition prescribes the values of the unknown function on the boundary of the domain. For an ordinary differential equation on $[a, b]$, it fixes $y(a)$ and $y(b)$. For a partial differential equation on a domain $\Omega$, it fixes $u$ on the boundary $\partial \Omega$. It is the most common type of condition in a boundary value problem, next to the Neumann and Robin conditions. See the definition.