Fabrice Bethuel

Fabrice Bethuel ( born June 7, 1963) is a French mathematician.

Bethuel was awarded his doctorate in 1989 with Jean -Michel Coron at the University of Paris-Sud. He is a professor at the University of Paris VI (Pierre et Marie Curie ).

Work

Bethuel became known for results on the density of continuous functions in the Sobolev space of maps between compact ( Riemannian ) manifolds, where he gave an accurate criterion that they are close in the Sobolev space already with his thesis. Then he looked at the issues of regularity of weakly stationary harmonic maps between Riemannian manifolds and showed that the dimension of the set of singular points equal is less than d-2, where d is the dimension of the output manifold of the figure. The requirement of stationarity is essential since his student T. Rivière showed that there is everywhere singular weakly harmonic maps in three and more dimensions. Previously, Frédéric Hélein had shown in 1990 that weakly harmonic maps of two-dimensional manifolds are regularly in spheres (1991 expanded by him in any pictures on Riemannian manifolds ) and Lawrence C. Evans, that for higher dimensions d of the output manifold weakly stationary harmonic spheres in pictures regularly up to singular quantities of the dimension d 2.

Bethuel also arrive, some with Haim Brezis, Frédéric Hélein and his pupil L. Almeida, major breakthroughs in the theory of Ginzburg -Landau equation. For example, they showed that the vortex for large values ​​of the parameter of the equation is determined by the values ​​of a renormalized energy. For work in this area was Bethuel student Sylvia Serfaty the EMS price.

His doctoral include Sylvia Serfaty and Tristan Rivière.

Awards

Won the 1999 Bethuel together with Frédéric Hélein the Fermat Prize for contributions to the calculus of variations. In 2002 he won the Prix Mergier - Bourdeix the Academie des Sciences. In 1998 he was invited speaker at the International Congress of Mathematicians in Berlin ( vortices in Ginzburg-Landau Equations ), and also in 1996 at the European Congress of Mathematicians in Budapest ( Some recent results on the Ginzburg-Landau Equation).

Writings

• Variational methods for Ginzburg-Landau Equations. In: Bethuel, Gerhard Huisken, Klaus Steffen, Stefan Müller: Calculus of Variations and geometric evolution problems. Cetraro 1996, Lecture Notes in Mathematics Volume 1713, Springer 1999
• With Hélein, Brezis: Ginzburg Landau vortices. Birkhäuser 1994
• The approximation problem- for Sobolev maps in between two manifolds. In: Acta Mathematica. Band 167, 1991, pp. 153-206