# Linear boundary value problem

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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.