BCAM Course

Sobolev inequalities for vector fields and injectively elliptic operators.

L¹ endpoint Sobolev estimates and cancelling operators.

Bourgain-Brezis duality estimates and cocancelling operators.

Proving the duality estimates.

L∞ estimates and connections with Hardy spaces.

Jean Van Schaftingen is a Belgian mathematical analyst whose research focuses on functional spaces and inequalities, the calculus of variations, and partial differential equations. His contributions span a wide range of topics, including Bourgain-Brezis endpoint Sobolev estimates, characterizations of Sobolev spaces, approximation, extension of traces, and lifting for Sobolev mappings between manifolds, Ginzburg-Landau relaxations, desingularization of vortices for the Euler and lake equations, symmetrization by rearrangement, semilinear elliptic equations of Schrödinger and Choquard type and homogenization.

After obtaining his doctoral degree in 2005 at UCLouvain under the supervision of Michel Willem, and completing a post-doctoral stay in Paris with Haïm Brezis, he joined UCLouvain as a professor in 2007. Since 2021, he has served as an ordinary professor and chair of the School of Mathematics. He has been awarded the Prix Adolphe Wetrems in 2011 and the Prix Jacques Deruyts in 2020 by the Académie royale des Sciences, des Lettres et des Beaux-Arts de Belgique.