Emmy Noether Lectures

1996 Lecturer: Ol’ga Oleinik

On Some Homogenization Problems For Differential Operators

Ol’ga Arsen’Enva Oleinik was born on July 2, 1925. She graduated from the Moscow State University in 1947, and continued her graduate work there. She received her Master’s degree in 1950, and her Doctor’s degree in 1954.

She is a member of the Russian Academy of Sciences, and a foreign member of the Academia Nazionale dei Lincei (Italy), Sachsische Academie of Sciences (Germany), Italian Academy of Sciences in Palermo (Italy), Italian Academy of Sciences in Milano, an honorary member of the Royal Society of Edinburgh (United Kingdom), and an honorary Doctor of the University of Rome. She was awarded a medal of College de France and a medal of the first degree at the Charles University in Prague. She also received the Chebotarev prize, State prize, Lomonosov prize, Petrowsky prize, and the prize of the Russian Academy of Sciences.

Oleinik’s main research is concerned with algebraic geometry, partial differential equations, and mathematical physics. Her early research was in algebraic geometry. Jointly with Petrovskii, she obtained the Euler characteristic of an (n-1)-dimensional algebraic surface of order m in a projective n-space. Her work on partial differential equations is fundamental and extremely broad. For example, she established a result on the coincidence of sets of regular points for second order linear elliptic equations, constructed a full theory of discontinuous solutions of non-linear hyperbolic equations, developed thr theory of second order linear equations with non-negative characteristic form, gave a solution to the question of hypoellipticity of second order elliptic equations of general form, and obtained profound results on the analyticity of solutions of linear equations and systems.

Oleinik has always been interested in applied problems. She constructed mathematical theories of non-stationary filtration of liquids and gases in porous media and also for the boundary layer, studied the Stefan’s problem on the distribution of heat in bodies in different phases, as well as problems in elasticity theory and homogenization.

Oleinik has published over three hundred papers and eight books. The most recent books are:

1. Mathematical problems in elasticity and homogenization, North-Holland, Amsterdam, 1992,

2. Homogenization of differential operators and integral functionals, Springer-Verlag, 1994, and

3. Some asymptotic problems of the theory of partial differential equations, Cambridge University Press, 1995.

Oleinik is a very successful teacher, having had fifty-eight thesis students. She is described by her colleagues as a woman of great personal charm, and is characterized by her sympathy and good nature in her relations with other people.