Hans Lewy Selecta
Volume 2
Herausgegeben: Kinderlehrer, David
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The work of Hans Lewy (1904--1988) has had a profound influence inthe direction of applied mathematics and partial differentialequations, in particular, from the late 1920s. Two of the particularsare well known. The Courant--Friedrichs--Lewy condition (1928), or CFLcondition, was devised to obtain existence and approximation results.This condition, relating the time and spatial discretizations forfinite difference schemes, is now universally employed in thesimulation of solutions of equations describing propagation phenomena.Lewy's example of a linear equation with no solution (1957), with its...
The work of Hans Lewy (1904--1988) has had a profound influence inthe direction of applied mathematics and partial differentialequations, in particular, from the late 1920s. Two of the particularsare well known. The Courant--Friedrichs--Lewy condition (1928), or CFLcondition, was devised to obtain existence and approximation results.This condition, relating the time and spatial discretizations forfinite difference schemes, is now universally employed in thesimulation of solutions of equations describing propagation phenomena.Lewy's example of a linear equation with no solution (1957), with itsattendant consequence that most equations have no solution, was notmerely an unexpected fact, but changed the viewpoint of the entirefield.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 ofboundary value problems, and several complex variables.He was amongthe first to study variational inequalities. In much of his work, hisunderlying philosophy was that simple tools of function theory couldhelp one understand the essential concepts embedded in an issue,although at a cost in generality. This approach was extremelysuccessful.In this two-volume work, most all of Lewy's papers are presented,in chronological order. They are preceded by several short essaysabout Lewy himself, prepared by Helen Lewy, Constance Reid, and DavidKinderlehrer, 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 hishonorary degree from the University of Bonn.
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