Exploring the Unknown: the Work of Louis Nirenberg on Partial Differential Equations

摘要

Partial differential equations are central objects in the mathematicalmodeling of natural and social sciences (sound propagation, heat diffusion,thermodynamics, electromagnetism, elasticity, fluid dynamics, quantummechanics, population growth, finance...etc). They were for a long timerestricted only to the study of natural phenomena or questions pertaining togeometry, before becoming over the course of time, and especially in the lastcentury, a field in itself. The second half of the XXth century was the "goldenage" of the exploration of partial differential equations from a theoreticalperspective. The mathematical work of Louis Nirenberg since the early 1950s hasto a large extent contributed to the growth of this fundamental area of humanknowledge. The name Nirenberg is associated with many of the milestones in thestudy of PDEs. The award of the Abel Prize to Louis Nirenberg marks a specialoccasion for us to revisit the development of the field of PDEs and the work ofone of the main actors of its exploration.