These notes are an expanded version of a series of ten talks I gave at an
NSF-CBMS Regional Conference on June 27-July 1, 1988, at Loyola Uni-
versity of Chicago. Additional, advanced lectures were presented by Emilio
Acerbi, Mike Crandall, Irene Fonseca, Nicola Fusco, Ron Gariepy, David
Kinderlehrer, Fang Hua Lin, Takis Souganidis, and Luc Tartar, all of whom
I wish to thank.
Let me also thank Nick Barron for initiating, organizing, and managing
the Conference. Nick is an expert in theoretical stochastic control theory, and
I can attest now to his great practical skills in this field as well. Many thanks
are due as well to Tanja Kazan for translating my fully nonlinear handwriting
into these typed notes.
I have corrected all known errors and typos in this latest printing, clarified
notation, and added references to some recent papers.
This work was supported in part by NSF grants DMS-86-10730 and CDR-
Lawrence C. Evans