View source for Neumann boundary conditions

{{TEX|done}}
''Neumann conditions, Neumann data, boundary conditions of the second kind''

Consider a second-order partial differential equation $Lu=f$ on a domain $D$ in $\mathbf R^n$ with boundary $S$ (cf. also [[Differential equation, partial, of the second order|Differential equation, partial, of the second order]]). Boundary conditions of the type

$$\frac{\partial u(x)}{\partial n}=\phi(x),\quad x\in S,$$

where $n$ is the outward pointing normal at $x$, are called Neumann boundary conditions.

A boundary value problem with Neumann conditions is also called a boundary value problem of the second kind (see [[Second boundary value problem|Second boundary value problem]]).

See also [[First boundary value problem|First boundary value problem]]; [[Dirichlet boundary conditions|Dirichlet boundary conditions]]; [[Third boundary value problem|Third boundary value problem]].