The work of Hans Lewy (1904--1988) has had a profound influence in
the direction of applied mathematics and partial differential
equations, in particular, from the late 1920s. Two of the particulars
are well known. The Courant--Friedrichs--Lewy condition (1928), or CFL
condition, was devised to obtain existence and approximation 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.
Lewy's 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 regularity theory of elliptic equations and systems, the Monge--
AmpSre Equation, the Minkowski Problem, the asymptotic analysis of
boundary value problems, and several 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 one understand the essential concepts embedded in an issue,
although at a cost in generality. This approach was extremely
successful.
In this two-volume work, most all of Lewy's papers are presented,
in chronological order. They are preceded by several short essays
about Lewy himself, prepared by Helen Lewy, Constance Reid, and David
Kinderlehrer, and commentaries on his work by Erhard Heinz, Peter Lax,
Jean Leray, Richard MacCamy, Fran?ois Treves, and Louis Nirenberg.
Additionally, there are Lewy's own remarks on the occasion of his
honorary degree from the University of Bonn.