Dr Filip Rindler
Filip RindlerWarwick Zeeman Lecturer
Office: B2.20 |
Teaching Responsibilities 2014/15:
Term 2: MA4G6 Calculus of Variations
Career
2014 - current: EPSRC Research Fellow
2013 - current: Zeeman Lecturer (Assistant Professor) in Mathematics, University of Warwick
2011 - current (on leave): 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 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".
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, also with the constraint of positivity of the determinant
- Compensated compactness and, more generally, restrictions on oscillations and concentrations
- Generalized Young measures
- Fine properties of functions of bounded variation/deformation
- Rigidity and softness, convex integration
- Rate-independent systems and their optimal control
Slides from talks about several aspects of my research can be found below.
Journal Publications:
[J14] K. Koumatos, F. Rindler, and E. Wiedemann: Differential inclusions and Young measures involving prescribed Jacobians. SIAM J. Math. Anal., to appear. Preprint.
[J13] K. Koumatos, F. Rindler, and E. Wiedemann: Orientation-preserving Young measures, submitted. Preprint.
[J12] J. Kristensen and F. Rindler: Piecewise affine approximations for functions of bounded variation. Preprint (revised version to follow shortly).
[J11] F. Rindler and G. Shaw: Strictly continuous extensions of functionals with linear growth to the space BV. Q. J. Math, 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.
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.
[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.
[N2] The positive Jacobian constraint in elasticity theory and orientation-preserving Young measures, Lecture Notes (SWRPDEWS Oxford), January 2014. Download.
[N1] Some differential inclusions for the gradient and the symmetrized gradient, Notes, December 2010 (revised January 2012). Download.