Welcome

I am Jean Van Schaftingen. I am professor of mathematics at the Université catholique de Louvain (UCLouvain). I am chair of the School of Mathematics at UCLouvain

I teach mathematical analysis to undergraduate students. I am currently teaching functional analysis, harmonic analysis, numerical analysis, measure theory, introduction to mathematical approach, history and epistemology of mathematics. I have taught analysis of functions of a single and several variables, ordinary differential equations, partial differential equations, calculus, complex numbers.

My research involves the mathematical analysis of problems in the calculus of variations and partial differential equations. These problems are inspired by quantum physics, liquid crystal models, computer graphics, fluid dynamics and differential geometry, to name a few. Unlike algebraic equations, the unknown in these equations is a function rather than a number. As there is no formula for the solving such problems and only approximate solutions can be computed, our aim is to determine the existence of solutions, whether they are unique, how they depend on the parameters and whether they have any symmetry properties. To achieve this, we must relate the different quantities appearing in the problem through inequalities and understand the functional spaces in which we are searching for a solution.

Among my publications, you will find a characterisation of the operators for which endpoint Sobolev inequalities hold; a justification of vortex-point dynamics for the lake equations as a limit of classical solutions; the semi-classical limit in nonlinear Schrödinger and Choquard equations; and approximation, lifting and extension of traces for Sobolev mappings.

In mathematical research evidence takes the form of a mathematical proof, and this means you either have it completely or not at all. In practice this means that lots of ideas that seemed promising in my brain, on the blackboard or in the margins turn out to be much more subtle if not completely wrong when I write them down on my computer. Many of the problems I have worked on are critical, meaning that some quantities are miraculously finite. This implies that any slightly wrong turn at any step will cause the proof miserably blow up.