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Welcome to the webpage of the ERC-funded project “SINGULARITY – Singularities and Compactness in Nonlinear PDEs” (2018 – 2024)!

The team is primarily based at the Mathematics Institute of the University of Warwick.

Our primary funding is from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement 757254), but we also gratefully acknowledge previous funding from the Engineering and Physical Sciences Research Council (EPSRC) and the Lloyds Register Foundation (LRF).

More information:





11/01/22 New preprint: Representation of the total variation as a Γ-limit of BMO-type seminorms by Adolfo Arroyo-Rabasa, Paolo Bonicatto, Giacomo Del Nin, Preprint.

01/10/21 New preprint: Energetic solutions to rate-independent large-strain elasto-plastic evolutions driven by discrete dislocation flow by Filip Rindler, Preprint.

28/09/21 New preprint: Space-time integral currents of bounded variation by Filip Rindler, Preprint.

21/09/21 New preprint: Elasto-plastic evolution of single crystals driven by dislocation flow by Thomas Hudson, Filip Rindler, Preprint.

19/07/21 New preprint: Advection-diffusion equation with rough coefficients: weak solutions and vanishing viscosity by Paolo Bonicatto, Gennaro Ciampa, Gianluca Crippa, Preprint.

17/06/21 New preprint: A Bourgain-Brezis-Mironescu representation for functions with bounded deformation by Adolfo Arroyo-Rabasa, Paolo Bonicatto, Preprint.

09/06/21 New preprint: Higher integrability for measures satisfying a PDE constraint by Adolfo Arroyo-Rabasa, Guido De Philippis, Jonas Hirsch, Filip Rindler, Anna Skorobogatova. Preprint.

23/04/21 New preprint: Endpoint Fourier restriction and unrectifiability by Giacomo Del Nin and Andrea Merlo, Preprint.

23/04/21 New preprint: Decomposition of integral metric currents by Paolo Bonicatto, Giacomo Del Nin and Enrico Pasqualetto, Preprint.

22/02/21 New preprint: Shape optimization of light structures and the vanishing mass conjecture by Jean-Francois Babadjian, Flaviana Iurlano, Filip Rindler, Preprint.

12/02/21 New preprint: Continuum limits of discrete isoperimetric problems and Wulff shapes in lattices and quasicrystal tilings by Giacomo Del Nin, Mircea Petrache, Preprint.

08/02/21 The project has been extended to 2024!

20/10/20 New team member: Paolo Bonicatto joins us as a postdoc from the University of Basel. Welcome!

09/10/20 New preprint: Slicing and fine properties of functions with bounded A-variation by Adolfo Arroyo-Rabasa,

01/06/20 The website has moved to its new host, directly at the University of Warwick.

29/05/20 New preprint: Debye screening for the stationary Vlasov-Poisson equation in interaction with a point charge by Adolfo Arroyo-Rabasa, Raphael Winter,

29/05/20 New preprint: Probabilistic solution of chaotic dynamical system inverse problems using Bayesian Artificial Neural Networks by David K. E. Green, Filip Rindler,

05/02/20 New preprint: Rectifiability of the jump set of locally integrable functions by Giacomo Del Nin,

05/02/20 New preprint: Geometric criteria for C^{1,α} rectifiability by Giacomo Del Nin, Kennedy Obinna Idu,

20/11/19 New preprint: On the fine properties of elliptic operators by Adolfo Arroyo Rabasa, Anna Skorobogatova,

5/11/19 New preprint: Fine properties of functions of bounded deformation – an approach via linear PDEs by Guido De Philippis, Filip Rindler,

12/09/19 New preprint: Quasiconvexity, null Lagrangians, and Hardy space integrability under constant rank constraintsby Andre Guerra, Bogdan Raita,

1/09/19 New team member: Giacomo Del Nin joins us as a postdoc from the University of Pisa. Welcome!

19/08/19 New preprint: Characterization of generalized Young measures generated by A-free measures by Adolfo Arroyo-Rabasa,

17/07/19 New preprint: Two-speed solutions to non-convex rate-independent systems by Filip Rindler, Sebastian Schwarzacher, Juan J. L. Velazquez,

06/05/19 New preprint: Concentration versus oscillation effects in brittle damage by Jean-Francois Babadjian, Flaviana Iurlano, Filip Rindler,

06/05/19 New preprint: A Note on Estimates for Elliptic Systems with L1 Data by Bogdan Raita, Daniel Spector,

06/05/19 New preprint: Model inference for ordinary differential equations by parametric polynomial kernel regression by David K. E. Green, Filip Rindler, Preprint

30/03/19 New preprint: On limiting trace inequalities for vectorial differential operators by Franz Gmeineder, Bogdan Raita, Jean Van Schaftingen,

15/03/19 New preprint: On the relaxation of integral functionals depending on the symmetrized gradient by Kamil Kosiba, Filip Rindler,

11/1/19 New preprint: Continuity and canceling operators of order n on ℝ^nby Bogdan Raita, Anna Skorobogatova,

4/2/19 New preprint: Generalized multi-scale Young measures by Adolfo Arroyo-Rabasa, Johannes Diermeier,

10/01/19 New preprint: An elementary approach to the dimension of measures satisfying a first-order linear PDE constraint by Adolfo Arroyo-Rabasa,

10/01/19 New preprint: L1-estimates for constant rank operators by Bogdan Raita,

22/11/18 Postdoc job available! We are looking for a Postdoctoral Research Fellow to join the team at the University of Warwick! The ideal candidate will have a strong background in the theory of PDEs, calculus of variations and potentially the theory of microstructure in materials. The position is for 24 months with the possibility of an extension for another 12 months. The closing date is 7 Jan 2019. Please see details and apply here.

12/11/18 New preprint: Dimensional estimates and rectifiability for measures satisfying linear PDE constraints by Adolfo Arroyo-Rabasa, Guido De Philippis, Jonas Hirsch, Filip Rindler,

15/10/18 Preprint: Critical L^p-differentiability of BV^𝔸-maps and canceling operators (revised) by Bogdan Raita,

28/06/18 Book Calculus of Variations by Filip Rindler has appeared with Springer! See for details.

05/06/18 New preprint: Relaxation for partially coercive integral functionals with linear growth by Filip Rindler, Giles Shaw,

06/04/18 New preprint: On the two-state problem for general differential operators by Guido De Philippis, Luca Palmieri, Filip Rindler,

01/04/18 New team members: Adolfo Arroyo-Rabasa (Leipzig) and Bogdan Raita (Oxford) will join the project as postdocs in autumn. Welcome!

01/04/18 Project now officially underway: The funding has officially started!

24/12/17 Survey article online: You can read a more technical description of some recent results here: AfreeSurvey.

03/12/17 Postdoc job available! We are looking for a Postdoctoral Research Fellow to join the team at the University of Warwick! The position is for 24 months with the possibility of an extension for another 12 months. Please apply here.

01/12/17 Website open!