Linear boundary value problem

2020 Mathematics Subject Classification: Primary: 34B05 [MSN][ZBL]

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.