Exploring the unknown: The work of Louis Nirenberg on partial differential equations

Abstract

Partial differential equations are central objects in the mathematical modeling of natural and social sciences (sound propagation, heat diffusion, thermodynamics, electromagnetism, elasticity, fluid dynamics, quantum mechanics, population growth, finance, etc.). They were for a long time restricted only to the study of natural phenomena or questions pertaining to geometry, before becoming over the course of time, and especially in the last century, a field in itself.

The second half of the 20th century was the “golden age” of the exploration of partial differential equations from a theoretical perspective. Louis Nirenberg, starting in the early 1950s, played a major role in the growth of this fundamental area of human knowledge and his name is associated with many of the milestones in the study of PDEs.

Louis Nirenberg passed away in January 2020 and his memory as a mathematician and colleague is a special invitation to review the development of the field of PDEs through the work of its leading pioneers.