Thematic Program on Partial Differential Equations
Coxeter Lecture Series
October 20 - 22, 2003
L. Craig Evans (Berkeley)
Three Singular Variational Problems
The Fields Institute
Coxeter Lecture Series (CLS) brings a leading mathematician to the Institute
to give a series of three lectures in the field of the current thematic
program. The first talk is an overview for a general mathematical audience,
postdoctoral fellows and graduate students. The other two talks are chosen,
in collaboration with the organizers of the thematic program, to target
specialists in the field.
Evans will introduce three related singular limit problems in the calculus
of variations, and explain their quite different interpretations. That
a common mathematical principle links these three problems suggests the
possibility of some unified methods for their analysis.
Lecture 1: Introduction, optimal mass transfer
Lecture 2: Weak KAM theory for dynamics
Lecture 3: Calculus of variations in the max-norm
L. Craig Evans, currently Miller Research Professor at the University
of California, Berkeley is a leading international figure in the theory
of nonlinear partial differential equations. His independent discovery
[Indiana Univ. Math. J 27 (1978) 875--887 and Israel Univ. Math. J.
36 (1980) 225--247] of the concept of viscosity solutions to second
order nonlinear elliptic equations brought him to prominence in the
field. The breadth of his contributions in more than 100 published articles
is overwhelming, as is the number of Ph.D. students and postdocs he
has supervised since his arrival at Berkeley in 1990. He is a leading
expositor on the subject, and has authored three influential books:
Weak Convergence Methods for Nonlinear Partial Differential Equation,
CBMS #74 American Mathematical Society 1990 (3rd printing).
Measure Theory and Fine Properties of Functions (with R.F. Gariepy),
CRC Press 1991 (2nd printing).
Partial Differential Equations, American Mathematical Society
1998 (2nd printing).
Worn copies may be found on the shelves of every researcher in the subject,
and they play a key role in current graduate education.