Hans Lewy Selecta: Volume 1

ISBN-13: 9781461274063 / Angielski / Miękka / 2011 / 358 str.

David Kinderlehrer

Opis

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.

Spis treści

Preface * Hans Lewy Opera * Hans Lewy: A Brief Biographical Sketch / David Kinderlehrer * The Music in Hans Lewy's Life / Helen Lewy * Hans Lewy: 1904--1988 / Constance Reid * Commentary on Lewy's Papers / Erhard Heinz * Hyperbolic Difference Equations: A Review of the Courant--Freidrichs--Lewy Paper in the Light of Recent Developments / Peter D. Lax * Les Premiers Travaux de Hans Lewy / Jean Leray * Confluence of Boundary Conditions / Richard MacCamy * Comments on Some of Hans Lewy's Work / Louis Nirenberg * Three Discoveries and One Question of Hans Lewy in CR Analysis / François Treves * Crisis in Mathematics / Hans Lewy * Selected Publications of Hans Lewy

O autorze

The work of Hans Lewy (1904--1988) has touched nearly every significant area of functional analysis and has had a profound influence in the direction of applied mathematics and partial differential equations from the late 1920s. Famous for his originality and ingenuity, Lewy illustrated and revealed fundamental principles on the theory of partial differential equations, in particular, on elliptic equations and free boundary problems. The papers presented in this two-volume set represent a selection of his best work and are augmented by commentary from his students, colleagues, and family.