Glimpses of nonlinear partial differential equations in the twentieth century. A priori estimates and the Bernstein problem

Research Report MRR00-025

Glimpses of nonlinear partial differential equations in the twentieth century. A priori estimates and the Bernstein problem

Neil S. Trudinger

Abstract: The theory of nonlinear partial differential equations has grown in relative importance within mathematics and its applications during the last century. Rather than being a unified theory, it is an assembly of various themes with wide ranging impact in other areas of mathematics as well as in finance, science and technology. In this talk we track developments from early in the century by Sergei Bernstein, through breakthroughs by De Giorgi, Krylov and Safonov and others, to recent discoveries, inspired by Bernstein's original work.

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