Dr Filip Rindler

Career

  • 2011-2015: Research Fellow at Gonville & Caius College, University of Cambridge (also member of DAMTP, CCA)
  • 2009-2011: DPhil student at the Oxford Centre for Nonlinear PDE (OxPDE), University of Oxford
  • 2004-2008: Undergraduate mathematics student at Technical and Humboldt Universities, Berlin, Germany

A full CV can be found here.

Research

Nonlinear Partial Differential Equations and the modern theory of the Calculus of Variations, in particular:

  • Lower semicontinuity and quasiconvexity
  • Generalized Young measures
  • Fine properties of functions of bounded variation/deformation
  • Rigidity arguments
  • Dimension reduction
  • Rate-independent systems and their optimal control 

At the core of my research is the study of singularities occurring in PDEs, in particular what can be rigorously proved about their "shape". Slides showing a few aspects of my research can be found below.

Publications

[10] F. Rindler: Characterization of Young measures generated by sequences in BV and BD, submitted (December 2011). Preprint.

[9] C. Kreisbeck and F. Rindler: Thin-film limits on A-free vector fields, submitted (May 2011). Preprint.

[8] F. Rindler: Lower semicontinuity for integral functionals in the space of functions of bounded deformation via rigidity and Young measures, Arch. Ration. Mech. Anal. 202 (2011), pp. 63-113. Online version.

[7] F. Rindler: Lower semicontinuity and Young measures in BV without Alberti’s Rank-One Theorem, Adv. Calc. Var., to appear (submitted February 2010). Online version.

[6] J. Kristensen and F. Rindler: Characterization of generalized gradient Young measures in W1,1 and BV, Arch. Ration. Mech. Anal. 197 (2010), pp. 539-598. Online version.

[5] J. Kristensen and F. Rindler: Relaxation of signed integral functionals in BV, Calc. Var. Partial Differential Equations 37 (2010), pp. 29-62. Online version.

[4] F. Rindler: Approximation of rate-independent optimal control problems, SIAM J. Numer. Anal. 47 (2009), pp. 3884-3909. Online version.

[3] A. Mielke and F. Rindler: Reverse Approximation of Energetic Solutions to Rate-Independent Processes, NoDEA Nonlinear Differential Equations Appl. 16 (2009), pp. 17-40. Online version.

[2] F. Rindler: Optimal Control for Nonconvex Rate-Independent Evolution Processes, SIAM J. Control Optim. 47 (2008), pp. 2773-2794. Online version.

[1] F. Rindler, M. Kubisch, E. Carlson, and D. Hollos: On the Proper Interference Protection in Wireless Multi-Hop Networks, Proceedings of the IEEE Wireless Communications and Networking Conference (WCNC) 2007, pp. 452-457. Online version.

Theses / Slides / Notes

[T2] Lower Semicontinuity and Young Measures for Integral Functionals with Linear Growth, DPhil thesis, University of Oxford, November 2011. Download.

[T1] Reverse Approximation of Rate-Independent Evolution Processes, Diploma thesis (Diplomarbeit), Technical University Berlin, September 2008. Download.

[S1] Lower semicontinuity for minimization problems in the space BD of functions of bounded deformation, Slides, November 2011. Download.

[N1] Some differential inclusions for the gradient and the symmetrized gradient, Notes, December 2010 (revised January 2012). Download.