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Dr Filip Rindler

  F.R. Portrait

Filip Rindler

Warwick Zeeman Lecturer



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

 

Teaching Responsibilities 2015/16:
None


Career

2014 - current: EPSRC Research Fellow

2013 - current: Zeeman Lecturer (Assistant Professor) in Mathematics, University of Warwick

2011 - 2015 (on leave 2013 - 2015): Drosier Research Fellow (JRF) in Mathematics at Gonville & Caius College, University of Cambridge (DAMTP, CCA)

2009 - 2011: DPhil student at the Oxford Centre for Nonlinear PDE (OxPDE), University of Oxford

2004 - 2008: Undergraduate student in mathematics and computer science 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".

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

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

Journal Publications:

[J16] G. De Philippis and F. Rindler: On the structure of A-free measures and applications. Preprint.

[J15] F. Rindler: Analysis of a two-speed model for finite-strain plasticity, submitted. Preprint.

[J14] K. Koumatos, F. Rindler, and E. Wiedemann: Orientation-preserving Young measures, submitted. Preprint.

[J13] K. Koumatos, F. Rindler, and E. Wiedemann: Differential inclusions and Young measures involving prescribed Jacobians. SIAM J. Math. Anal. 47 (2015), pp. 1169-1195. Online version.

[J12] J. Kristensen and F. Rindler: Piecewise affine approximations for functions of bounded variation. Numer. Math. 2015, to appear. Preprint.

[J11] F. Rindler and G. Shaw: Strictly continuous extensions of functionals with linear growth to the space BV. Q. J. Math. 00 (2015), pp. 1-26, to appear.

[J10] C. Kreisbeck and F. Rindler: Thin-film limits of functionals on A-free vector fields. Indiana Univ. Math. J., to appear. Online version.

[J9] F. Rindler: Directional oscillations, concentrations, and compensated compactness via microlocal compactness forms. Arch. Ration. Mech. Anal. 215 (2015), pp. 1-63. Online version.

[J8] F. Rindler: A local proof for the characterization of Young measures generated by sequences in BV, J. Funct. Anal. 266 (2014), pp. 6335-6371. Online version.

[J7] 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.

[J6] 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.

[J5] J. Kristensen and F. Rindler: Characterization of generalized gradient Young measures in W^{1,1} and BV, Arch. Ration. Mech. Anal. 197 (2010), pp. 539-598. Online version.

[J4] J. Kristensen and F. Rindler: Relaxation of signed integral functionals in BV, Calc. Var. Partial Differential Equations 37 (2010), pp. 29-62. Online version.

[J3] F. Rindler: Approximation of rate-independent optimal control problems, SIAM J. Numer. Anal. 47 (2009), pp. 3884-3909. Online version.

[J2] 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.

[J1] F. Rindler: Optimal Control for Nonconvex Rate-Independent Evolution Processes, SIAM J. Control Optim. 47 (2008), pp. 2773-2794. Online version.

Further refereed & non-refereed proceedings publications can be found in my CV.

Lecture Notes (currnt versions) / Theses / Slides

[N3] Introduction to the Modern Calculus of Variations, Lecture Notes, April 2015. Download.

[N2] The positive Jacobian constraint in elasticity theory and orientation-preserving Young measures, Lecture Notes, August 2015. Download.

[N1] Some differential inclusions for the gradient and the symmetrized gradient, Notes, January 2012. Download.

[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.

[S3] The positive Jacobian constraint in elasticity theory and orientation-preserving Young measures, Slides, January 2014. 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.