Fabrice Béthuel
Fabrice Béthuel (born June 7, 1963 ) is a French mathematician .
Béthuel received his doctorate in 1989 under Jean-Michel Coron at the University of Paris-South . He is a professor at the University of Paris VI (Pierre et Marie Curie).
plant
Béthuel already became known with his dissertation for results regarding the density of continuous functions in the Sobolew space of the mappings between compact (Riemannian) manifolds , where he specified an exact criterion that they are dense in the Sobolew space. Then he dealt with questions of the regularity of weak harmonic stationary mappings between Riemannian manifolds and showed that the dimension of the set of singular points is less than or equal to d − 2, where d is the dimension of the output manifold of the map. The requirement of stationarity is essential, as his student T. Rivière showed that there are singular, weakly harmonic images in three and more dimensions everywhere. Earlier, Frédéric Hélein shown in 1990 that weakly harmonic maps of two-dimensional manifolds in spheres are regularly (1991 expanded by him on illustrations in any Riemannian manifolds) and Lawrence C. Evans that higher dimensions of the output manifold d weak harmonic stationary pictures in spheres are regular except for singular sets of dimension d − 2.
Bethuel also achieved important breakthroughs in the theory of the Ginzburg-Landau equation , partly with Haïm Brezis , Frédéric Hélein and his student L. Almeida . For example, they showed that for large values of the parameter of the equation, the vortex is determined by the values of a renormalized energy. Béthuel's student Sylvia Serfaty received the EMS Prize for work in this area .
His PhD students include Sylvia Serfaty and Tristan Rivière .
Awards
In 1999, Béthuel and Frédéric Hélein won the Fermat Prize for contributions to the calculus of variations . In 2002 he won the Prix Mergier-Bourdeix of the Académie des sciences . In 1998 he was invited speaker at the International Congress of Mathematicians in Berlin ( Vortices in Ginzburg-Landau Equations ) and also at the 1996 European Congress of Mathematicians in Budapest ( Some recent results on the Ginzburg-Landau Equation ).
Fonts
- Variational methods for Ginzburg-Landau equations. In: Bethuel, Gerhard Huisken , Klaus Steffen , Stefan Müller : Calculus of Variations and geometric evolution problems (= Lecture Notes in Mathematics. 1713 = Lectures given at the Session of the Centro Internazionale Matematico Estivo (CIME). 2). Springer, Berlin et al. 1999, ISBN 3-540-65977-3 , pp. 1-43, doi : 10.1007 / BFb0092668 .
- with Frédéric Hélein , Haïm Brezis : Ginzburg-Landau Vortices (= Progress in non-linear Differential Equations and their Applications. 13). Birkhäuser, Boston MA et al. 1994, ISBN 0-8176-3723-0 .
- The approximation problem for Sobolev maps between two manifolds. In: Acta Mathematica . Vol. 167, 1991, pp. 153-206, doi : 10.1007 / BF02392449 .
Web links
Individual evidence
- ↑ Bethuel, Xiaomin Zheng: Density of smooth functions between two manifolds in Sobolev space. In: Journal of Functional Analysis. Vol. 80, No. 1, 1988, pp. 60-75, doi : 10.1016 / 0022-1236 (88) 90065-1 .
- ↑ Fabrice Béthuel in the Mathematics Genealogy Project (English)
| personal data | |
|---|---|
| SURNAME | Béthuel, Fabrice |
| BRIEF DESCRIPTION | French mathematician |
| DATE OF BIRTH | June 7, 1963 |