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Dr Filip Rindler

  F.R. Portrait

Filip Rindler

Associate Professor
ATI Faculty Fellow


Office: B2.20
 Phone: +44 (0) 2476 5 28328
 Email: F dot Rindler at warwick dot ac dot uk

 

Teaching Responsibilities 2016/17:
Term 2: MA4G6 Calculus of Variations


Research

Most of my research concerns singularities in nonlinear PDEs and the modern theory of the calculus of variations. In particular, I am interested in oscillation and concentration phenomena and what can be rigorously proved about their "shape". Applications include elasticity and elasto-plasticity theory.

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
  • Fine properties of functions of bounded variation/deformation
  • Rigidity and softness, convex integration
  • Rate-independent systems and plasticity

I also worked on telecommunications networks and have recently become interested in anomaly detection in streaming data.

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

 

Recent preprints

  • On a conjecture of Cheeger (with G. De Philippis and A. Marchese), to appear in "Measure Theory in Non-Smooth Spaces" (Nicola Gigli, ed.), De Gruyter, Preprint.
  • Characterization of Young measures generated by functions of bounded deformation (with G. De Philippis), Preprint.
  • Existence and regularity for a class of rate-independent systems (with S. Schwarzacher), Preprint.

 

Selected publications

  • On the structure of A-free measures and applications (with G. De Philippis), Ann. of Math. 184 (2016), 1017-1039, Online version.
  • Differential inclusions and Young measures involving prescribed Jacobians (with K. Koumatos, E. Wiedemann), SIAM J. Math. Anal. 47 (2015), 1169-1195. Online version.
  • Directional oscillations, concentrations, and compensated compactness via microlocal compactness forms. Arch. Ration. Mech. Anal. 215 (2015), 1-63. Online version.
  • A local proof for the characterization of Young measures generated by sequences in BV, J. Funct. Anal. 266 (2014), 6335-6371. Online version.
  • Lower semicontinuity and Young measures in BV without Alberti’s Rank-One Theorem, Adv. Calc. Var. 5 (2012), 127-159. Online version.
  • Lower semicontinuity for integral functionals in the space of functions of bounded deformation via rigidity and Young measures, Arch. Ration. Mech. Anal. 202 (2011), 63-113. Online version.
  • Characterization of generalized gradient Young measures in W^{1,1} and BV (with J. Kristensen), Arch. Ration. Mech. Anal. 197 (2010), 539-598. Online version.
  • Relaxation of signed integral functionals in BV (with J. Kristensen), Calc. Var. Partial Differential Equations 37 (2010), 29-62. Online version.
  • Optimal control for nonconvex rate-independent evolution processes, SIAM J. Control Optim. 47 (2008), 2773-2794. Online version.

A complete list of publications can be found in my CV.

 

Lecture notes / theses / slides

  • Introduction to the Modern Calculus of Variations, Lecture notes for a 30h fourth-year module, April 2015. Download.
  • The positive Jacobian constraint in elasticity theory and orientation-preserving Young measures, Lecture notes for a short course, August 2015. Download.
  • Lower Semicontinuity and Young Measures for Integral Functionals with Linear Growth, DPhil thesis, University of Oxford, November 2011. Download.
  • Reverse Approximation of Rate-Independent Evolution Processes, Diploma thesis, Technical University Berlin, September 2008. Download.
  • On the structure of PDE-constrained measures and applications, Slides, June 2016. Download.
  • The positive Jacobian constraint in elasticity theory and orientation-preserving Young measures, Slides, January 2014. Download.
  • Directional oscillations and concentrations and weak/strong compactness via microlocal compactness forms, Slides, December 2012. Download.
  • Lower semicontinuity for minimization problems in the space BD of functions of bounded deformation, Slides, November 2011. Download.