1994 Fields Medal (2)
Reason for Award
... such nonlinearpartial differential equationsimply do not have smooth or even C1 solutions existing after short times. ... The only option is therefore to search for some kind of "weak" solution. This undertaking is in effect to figure out how to allow for certain kinds of "physically correct" singularities and how to forbid others. ... Lions and Crandall at last broke open the problem by focusing attention onviscosity solutions, which are defined in terms of certain inequalities holding wherever the graph of the solution is touched on one side or the other by a smoothtest function
Laureates
Pierre-Louis Lions,
France
Other works in the same year
- Bourgain's work touches on several central topics of mathematical analysis: the geometry ofBanach spaces, convexity in high dimensions,harmonic analysis,ergodic theory, and finally, nonlinearpartial differential equationsfrommathematical physics.
- proving stability properties - dynamic stability, such as that sought for the solar system, orstructural stability, meaning persistence under parameter changes of the global properties of the system.
- For his solution to the restricted Burnside problem.