Research Interests

My mathematical research has been devoted to the study of solutions of nonlinear partial differential equations and to a variety of problems in mathematical physics and differential geometry, involving such equations. In the past decade, my students and I have investigated models arising in the Thomas-Fermi theory of atoms and molecules, in the theory of liquid crystals and in superconductors. This includes a detailed mathematical analysis of singularities: line and point defects, Ginzburg-Landau vortices, etc. In the closely related problems of global geometry, blow-up phenomena and the appearance of singularities are associated with critical exponents and lack of compactness in the variational formulation. I have been able to classify all possible singular behavior in many cases, using new techniques and ideas from various sectors of mathematics: calculus of variations, nonlinear functional analysis, estimates in Sobolev spaces of solutions of nonlinear partial differential equations, Fourier analysis and the topology of Sobolev manifolds.

Membership Type

International Member

Election Year

2003

Primary Section

Section 11: Mathematics

Secondary Section

Section 32: Applied Mathematical Sciences