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--AmpA]re 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, FranAois Treves, and Louis Nirenberg.
Additionally, there are Lewy's own remarks on the occasion of his
honorarydegree from the University of Bonn.
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