Professor Jan Kristensen

Background

I got an MSc in Engineering from the Technical University of Denmark and a PhD in Mathematics from the same university. After my PhD I worked as a temporary lecturer at Aalborg University (also in Denmark), and as postdoc at Heriot-Watt University and at University of Oxford. During this time I also spent some longer periods visiting the Max-Planck-Institute for Mathematics in the Sciences in Leipzig. From 2000 to 2003 I worked as lecturer in Mathematics at Heriot-Watt University, and since October 2003 I have been working here. I have held the title of Professor of Mathematics since October 2010.

Teaching

At the college I often give tutorials in Analysis and related topics for first and second year undergraduates. However I have over the years covered most of the first and second year undergraduate mathematics curriculum in tutorials. During Michaelmas and Hilary Terms I usually lecture undergraduate courses at the Mathematical Institute.

Research Interests

The general area of my work is Analysis. I am particularly interested in questions about existence and regularity of solutions to variational problems and the related partial differential equations.

Selected Publications

• J. Bourgain, M.V. Korobkov, J. Kristensen: On the Morse-Sard property and level sets of Sobolev and BV functions, Rev. Mat. Iberoam. 29 (2013), no. 1, 1–23
• J. Kristensen, G. Mingione: Boundary regularity in variational problems, Arch. Ration. Mech. Anal. 198 (2010), no. 2, 369–455
• J. Kristensen, F. Rindler: Characterization of generalized gradient Young measures generated by sequences in $W^{1,1}$ and $BV$,
  Arch. Ration. Mech. Anal. 197 (2010), no. 2, 539–598
• J. Kristensen, G. Mingione: The singular set of Lipschitzian minima of multiple integrals, Arch. Ration. Mech. Anal. 184 (2007), no. 2, 341-369
• F. Duzaar, J. Kristensen, G. Mingione: The existence of regular boundary points for non-linear elliptic systems, J. Reine Angew. Math. 602 (2007), 17–58
• J. Kristensen, G. Mingione: The singular set of minima of integral functionals, Arch. Ration. Mech. Anal. 184 (2006), no. 3, 331–398
• J. Kristensen, A. Taheri: Partial regularity of strong local minimizers in the multi-dimensional calculus of variations, Arch. Ration. Mech. Anal. 170 (2003), no. 1, 63–89
• J.M. Ball, B. Kirchheim, J. Kristensen: Regularity of quasiconvex envelopes, Calc. Var. Partial Differential Equations 11 (2000), no. 4, 333-359
• J. Kristensen: Lower semicontinuity in spaces of weakly differentiable functions, Math. Ann. 313 (1999), no. 4, 653–710
• J. Kristensen: On the non-locality of quasiconvexity, Ann. Inst. H. Poincare Anal. Non Lineaire 16 (1999), no. 1, 1–13