Paul Rabinowitz

Paul Henry Rabinowitz (born November 15, 1939 in Newark , New Jersey ) is an American mathematician who deals with partial differential equations, calculus of variations and dynamic systems.

Paul Rabinowitz, Oberwolfach 2005

Live and act

Rabinowitz studied at the Courant Institute of Mathematical Sciences of New York University , where he obtained his doctorate in 1966 under Jürgen Moser ( Periodic solutions of nonlinear hyperbolic differential equations ). He then went from January 1966 to 1969 as an assistant professor at Stanford University . In 1969 he went to the University of Wisconsin – Madison as an Associate Professor , where he has been a full professor since 1971. Since 1986 he has been the E. B. van Vleck Professor of Mathematics there. He was visiting professor in Aarhus , at the ETH Zurich (1982, 1994), in Paris (1972–1973) and in Pisa .

Rabinowitz is especially known for new results in the investigation of nonlinear systems. He proved a global bifurcation theorem (that is, he proved the existence of a “global” branched solution by considering the local, linearized theory). In 1977 he proved the existence of periodic solutions in Hamiltonian systems under the assumption that the energy surface is "star-shaped". With Michael Crandall , he proved a theorem about Hopf bifurcations in an infinite number of dimensions in the 1970s .

He developed the calculus of variations new mini-max methods on "indefinite problems" (which is not the Palais-Smale compactness condition comply) may be used by Rabinowitz for example, Hamiltonian systems, semilinear elliptical applied systems of nonlinear equations. In 1973 he and Antonio Ambrosetti proved the Mountain Pass Theorem .

In 1978/79 he was a Guggenheim Fellow. He is a member of the American Academy of Arts and Sciences (1987) and the National Academy of Sciences (1998) and an honorary doctorate from the University of Paris (1992). In 1984 he was a Colloquium Lecturer at the American Mathematical Society (AMS). In 1998 he received the Birkhoff Prize . In 1978 he was invited speaker at the International Congress of Mathematicians in Helsinki ( Critical points of indefinite functionals and periodic solutions of differential equations ). He is a fellow of the American Mathematical Society.

Web links

Homepage in Wisconsin ( Memento of October 7, 2008 in the Internet Archive )
On the awarding of the Birkhoff Prize to Rabinowitz (PDF file; 95 kB)

Individual evidence

↑ Michael G. Crandall , Rabinowitz: The Hopf bifurcation theorem in infinite dimensions. In: Archive for Rational Mechanics and Analysis. Volume 67, No. 1, 1977, pp. 53-72, doi : 10.1007 / BF00280827 .
^ Antonio Ambrosetti , Rabinowitz: Dual variational methods in the critical point theory and applications. In: Journal of Functional Analysis. Volume 14, No. 4, 1973, pp. 349-381, doi : 10.1016 / 0022-1236 (73) 90051-7 .
^ Youssef Jabri: The Mountain Pass Theorem. Variants, Generalizations and Some Applications (= Encyclopedia of Mathematics and its Applications. 95). Cambridge University Press, Cambridge et al. 2003, ISBN 0-521-82721-3 .

personal data
SURNAME	Rabinowitz, Paul
ALTERNATIVE NAMES	Rabinowitz, Paul Henry (full name)
BRIEF DESCRIPTION	American mathematician
DATE OF BIRTH	November 15, 1939
PLACE OF BIRTH	Newark , New Jersey

[1] Michael G. Crandall , Rabinowitz: The Hopf bifurcation theorem in infinite dimensions. In: Archive for Rational Mechanics and Analysis. Volume 67, No. 1, 1977, pp. 53-72, doi : 10.1007 / BF00280827 .

[2] Antonio Ambrosetti , Rabinowitz: Dual variational methods in the critical point theory and applications. In: Journal of Functional Analysis. Volume 14, No. 4, 1973, pp. 349-381, doi : 10.1016 / 0022-1236 (73) 90051-7 .

[3] Youssef Jabri: The Mountain Pass Theorem. Variants, Generalizations and Some Applications (= Encyclopedia of Mathematics and its Applications. 95). Cambridge University Press, Cambridge et al. 2003, ISBN 0-521-82721-3 .