The solution of boundary value problems by multiple Laplace transformations

By use of the multiple Laplace transform a partial differential equation and its associated boundary conditions characterizing a boundary value problem in n independent real variables can be transferred directly into an algebraic equation in n independent complex variables. This algebraic equation can be solved for the multiple transform of the solution of the boundary value problem. Multiple inversion of this transform then gives the desired solution. The general theory underlying such solution of boundary value problems in two and three independent variables is advanced in detail. Use of this theory is illustrated by solution of two specific problems.