Filip Rindler Professor of Mathematics   Office: B1.26  Phone: +44 (0) 2476 5 28328  Email: F dot Rindler at warwick dot ac dot uk

 

Research

My research sits at the intersection between Partial Differential Equations, Geometric Measure Theory, and the Calculus of Variations. In particular, I am interested in oscillation and concentration phenomena and what can be rigorously proved about their "shape". On the applied side, I am interested in the Mathematics of Material Science, in particular the theories of elasticity, elasto-plasticity and dislocations.

My research has been funded by the European Research Council (ERC), EPSRC, and the Lloyds Register Foundation.

Our group maintains the website www.ercsingularity.org, which contains details on our research, publications, and recent preprints.

 

Selected recent publications

• Energetic solutions to rate-independent large-strain elasto-plastic evolutions driven by discrete dislocation flow, to appear in J. Eur. Math. Soc. arXiv:2109.14416Link opens in a new window.
• Shape optimization of light structures and the vanishing mass conjecture (with J.-F. Babadjian, F. Iurlano), Duke Math. J. 172 (2023), 43-103. Online versionLink opens in a new window.
• Space-time integral currents of bounded variation, Calc. Var. Partial Differential Equations 62 (2023), Paper No. 54. Online versionLink opens in a new window.
• Elasto-plastic evolution of crystal materials driven by dislocation flow (with T. Hudson), Math. Models Methods Appl. Sci. (M3AS) 32 (2022), 851-910. Online versionLink opens in a new window.
• Concentration versus oscillation effects in brittle damage (with J.-F. Babadjian, F. Iurlano), Comm. Pure Appl. Math. 74 (2021), 1803-1854. Online versionLink opens in a new window.
• Two-speed solutions to non-convex rate-independent systems (with S. Schwarzacher, J. J. L. Velázquez), Arch. Ration. Mech. Anal. 239 (2021), 1667-1731. Online versionLink opens in a new window.
• Dimensional estimates and rectifiability for measures satisfying linear PDE constraints (with A. Arroyo-Rabasa, G. De Philippis, J. Hirsch), Geom. Funct. Anal. 29 (2019), pp 639-658. Online versionLink opens in a new window.
• Liftings, Young measures, and lower semicontinuity (with G. Shaw), Arch. Ration. Mech. Anal. 232 (2019), 1227-1328. Online versionLink opens in a new window.
• On the structure of A-free measures and applications (with G. De Philippis), Ann. of Math. 184 (2016), 1017-1039. Online versionLink opens in a new window.
• Directional oscillations, concentrations, and compensated compactness via microlocal compactness forms, Arch. Ration. Mech. Anal. 215 (2015), 1-63. Online versionLink opens in a new window.

 

Curriculum Vitae

 

Teaching

I usually teach Analysis courses at the University of Warwick (e.g. PDEs, Real Analysis, Geometric Measure Theory, Calculus of Variations, Complex Analysis).

The book Calculus of Variations is based on my lectures at the University of Warwick and appeared with Springer in 2018:

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See www.calculusofvariations.comLink opens in a new window for details.