Haim Brezis
Rutgers, The State University of New Jersey, New Brunswick
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Primary Section: 11, Mathematics Secondary Section: 32, Applied Mathematical Sciences Membership Type:
International Member
(elected 2003)
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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.
