Hans Lewy Selecta: Volume 1

The work of Hans Lewy (1904-1988) has had a profound influence in the direc­ tion of applied mathematics and partial differential equations, in particular, from the late 1920s. We are all familiar with two of the particulars. The Courant-Friedrichs­ Lewy condition (1928), or CFL condition, was devised to obtain existence and ap­ proximation results. This condition, relating the time and spatial discretizations for finite difference schemes, is now universally employed in the simulation of solutions of equations describing propagation phenomena. His example of a linear equation with no solution (1957), with its attendant consequence that most equations have no solution, was not merely an unexpected fact, but changed the viewpoint of the entire field. Lewy made pivotal contributions in many other areas, for example, the regu­ larity theory of elliptic equations and systems, the Monge-Ampere Equation, the Minkowski Problem, the asymptotic analysis of boundary value problems, and sev­ eral complex variables. He was among the first to study variational inequalities. In much of his work, his underlying philosophy was that simple tools of function theory could help us understand the essential concepts embedded in an issue, although at a cost in generality. This was extremely successful.