Dirichlet also studied the first boundary value problem, for the Laplace equation, proving the unicity of the solution; this type of problem in the theory of partial differential equations was later named the Dirichlet problem after him [REF].
While trying to gauge the range of functions for which convergence of the Fourier series can be shown, Dirichlet defines a function by the property that "to any x there corresponds a single finite y", but then restricts his attention to piecewise continuous functions.