Dr Filip Rindler

Career

  • 2011-2015: Drosier Research Fellow in Mathematics 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

Singularities in Nonlinear Partial Differential Equations and the modern theory of the Calculus of Variations. At the core of my research is the study of "singularities", here defined to mean oscillation and concentration phenomena. In particular, I am interested in what can be rigorously proved about their "shape".

I have prepared a short general overview over my research.

On a more technical level, I work on:

  • Efficient description of oscillations and concentrations
  • Lower semicontinuity and quasiconvexity
  • Compensated compactness and, more generally, restrictions on oscillations and concentrations
  • Generalized Young measures
  • Fine properties of functions of bounded variation/deformation
  • Rigidity arguments
  • Rate-independent systems and their optimal control

Slides from talks about several aspects of my research can be found below.

Publications

[11] F. Rindler: Directional oscillations, concentrations, and compensated compactness via microlocal compactness forms, submitted. Preprint (newest version 1.2).

[10] J. Kristensen and F. Rindler: Piecewise affine approximations for functions of bounded variation, submitted. Preprint (newest version 1.2).

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

[8] F. Rindler: Lower semicontinuity and Young measures in BV without Alberti’s Rank-One Theorem, Adv. Calc. Var. 5 (2012), pp.~127-159. Online version.

[7] 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.

[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.

[S2] Directional oscillations and concentrations and weak/strong compactness via microlocal compactness forms, Slides, December 2012. 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.