He introduced the concept of a well-posed initial value and boundary value problem.
The measurement process may cause a large number of values to take the boundary value.
His work on boundary value problems on differential equations is remembered because of what is called today Sturm Liouville theory which is used in solving integral equations.
He also worked on conformal mappings and potential theory, and he was led to study boundary value problems for partial differential equations and the theory of various functionals connected with them.
The boundary value problem was solved numerically and is displayed in Fig.6.