Abstract
This will be an expository lecture, surveying many important methods for passing to limits for solutions of various nonlinear PDE. I will illustrate several of these techniques as applied to some simple examples, and discuss also many open problems.
Brief Biography
Lawrence Craig Evans is a Professor of Mathematics at the University of California, Berkeley. His research is in the field of nonlinear partial differential equations, primarily elliptic equations. In 2004, he shared the Leroy P. Steele Prize for Seminal Contribution to Research with Nicolai V. Krylov for their proofs, found independently, that solutions of concave, fully nonlinear, uniformly elliptic equations are $C^{2, \alpha}$. Evans also made significant contributions to the development of the theory of viscosity solutions of nonlinear equations, to the understanding of the Hamilton–Jacobi–Bellman equation arising in stochastic optimal control theory, and to the theory of harmonic maps. He is also well known as the author of the textbook Partial Differential Equations, which is considered as a standard introduction to the theory at the graduate level. His textbook Measure theory and fine properties of functions (coauthored with Ronald Gariepy), an exposition on Hausdorff measure, capacity, Sobolev functions, and sets of finite perimeter, is also widely cited. Evans is an ISI highly cited researcher.
