View source for Linear boundary value problem

{{MSC|34B05}}
{{TEX|done}}

The problem of determining in a domain $D$ of the variable $x = (x_1,\ldots,x_n)$ the solution $u(x)$ of a linear differential equation
$$
(Lu)(x) = f(x), \quad x\in D,
$$
which satisfies on the boundary $S$ of this domain (or on a part of it) the linear boundary conditions
$$
(Bu)(y) = \phi(y), \quad y\in S.
$$
See also [[Boundary value problem, ordinary differential equations]]; [[Boundary value problem, partial differential equations]].