The following text is from the memorial written for Professor DiPerna shortly after his death:
Ronald J. DiPerna, a professor of mathematics at the University of California at Berkeley, died in Princeton on January 8, 1989. At the time of his death he was a visiting member of the Institute for Advanced Study at Princeton, NJ. His wife, Maria Schonbeck, is a professor of mathematics at the University of California, Santa Cruz. They have one daughter, Lauren.
DiPerna was born in Sommerville, Massachusetts, on February 11, 1947. He received his Ph.D. at the Courant Institute of Mathematical Sciences of New York University in 1972, and held faculty positions at Brown University, the University of Michigan, the University of Wisconsin and Duke University before coming to Berkeley in 1985.
DiPerna was known for his work on nonlinear partial differential equations, especially those that are important in fluid dynamics and the kinetic theory of gases. Probably his best known work is his development and application of the method of compensated compactness. This is a very powerful method for controlling oscillation and thereby proving existence theorems. DiPerna proved existence of weak solutions in the large for the equations of compressible gas dynamics and obtained important results concerning the uniqueness of solutions, their large time behavior, and their local regularity as elements of the appropriate abstract spaces.
His recent work concerned integro-differential equations that arise in the kinetic theory of gases and certain types of singularity that arise in incompressible flow.
DiPerna's work is remarkable for the courage and vision with which he attacked and conquered problems of exceptional difficulty. His papers are masterpieces of hard analysis and a source of wonder and inspiration to all those who read them and learn from them. His dedication to mathematics is legendary, and his scientific vision permeates much of contemporary analysis. His very premature death deprives the mathematics community as a whole, and the mathematics department at Berkeley in particular, of a very important and innovative voice.
DiPerna held Guggenheim and Sloan fellowships; he spoke at the International Congress of Mathematicians, and was a member of the Institute for Advanced Study at Princeton. Had he lived, his work would have earned the highest honors that the mathematical community can bestow. The Mathematics Department at Berkeley keenly feels his loss.
Alexandre J. Chorin
Craig Evans
James Gilman
Andrew Majda
