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Mathematics Institute

Publications

Project publications

  • Advection-diffusion equation with rough coefficients: weak solutions and vanishing viscosity (Paolo Bonicatto, Gennaro Ciampa, Gianluca Crippa), Preprint.
  • A Bourgain-Brezis-Mironescu representation for functions with bounded deformation (Adolfo Arroyo-Rabasa, Paolo Bonicatto), Preprint.
  • Higher integrability for measures satisfying a PDE constraint (Adolfo Arroyo-Rabasa, Guido De Philippis, Jonas Hirsch, Filip Rindler, Anna Skorobogatova), Preprint.

  • Endpoint Fourier restriction and unrectifiability (Giacomo Del Nin and Andrea Merlo), Preprint.

  • Decomposition of integral metric currents (Paolo Bonicatto, Giacomo Del Nin and Enrico Pasqualetto), Preprint.

  • On the structure of divergence-free measures on R^2 (Paolo Bonicatto and Nikolay A. Gusev), Preprint.
  • Shape optimization of light structures and the vanishing mass conjecture (Jean-Francois Babadjian, Flaviana Iurlano, Filip Rindler), Preprint.
  • Continuum limits of discrete isoperimetric problems and Wulff shapes in lattices and quasicrystal tilings (Giacomo Del Nin, Mircea Petrache), Preprint.
  • Slicing and fine properties of functions with bounded A-variation (Adolfo Arroyo-Rabasa), Preprint
  • Debye screening for the stationary Vlasov-Poisson equation in interaction with a point charge (Adolfo Arroyo-Rabasa, Raphael Winter), Preprint
  • Probabilistic solution of chaotic dynamical system inverse problems using Bayesian Artificial Neural Networks (David K. E. Green, Filip Rindler), Preprint
  • Rectifiability of the jump set of locally integrable functions (Giacomo Del Nin), Preprint
  • Geometric criteria for C^{1,α} rectifiability (Giacomo Del Nin, Kennedy Obinna Idu), Preprint
  • On the fine properties of elliptic operators (Adolfo Arroyo Rabasa, Anna Skorobogatova), Preprint
  • Fine properties of functions of bounded deformation – an approach via linear PDEs (Guido De Philippis, Filip Rindler), Preprint
  • Quasiconvexity, null Lagrangians, and Hardy space integrability under constant rank constraints (A. Guerra, B. Raita), Preprint
  • Characterization of generalized Young measures generated by A-free measures (A. Arroyo-Rabasa), Preprint
  • Two-speed solutions to non-convex rate-independent systems (F. Rindler, S. Schwarzacher, J. J. L. Velazquez), Preprint
  • Concentration versus oscillation effects in brittle damage (J.-F. Babadjian, F. Iurlano, F. Rindler), Preprint
  • A Note on Estimates for Elliptic Systems with L1 Data (B. Raita, D. Spector), Preprint
  • Model inference for ordinary differential equations by parametric polynomial kernel regression (D. K. E. Green, F. Rindler), Preprint
  • On limiting trace inequalities for vectorial differential operators (F. Gmeineder, B. Raita, J. Van Schaftingen), Preprint.
  • On the relaxation of integral functionals depending on the symmetrized gradient (K. Kosiba, F. Rindler), Preprint
  • Continuity and canceling operators of order n on ℝ^n (B. Raita, A. Skorobogatova), Preprint.
  • Generalized multi-scale Young measures (A. Arroyo-Rabasa, J. Diermeier), Preprint
  • An elementary approach to the dimension of measures satisfying a first-order linear PDE constraint (A. Arroyo-Rabasa), Preprint.
  • L1-estimates for constant rank operators (B. Raita), Preprint.
  • Dimensional estimates and rectifiability for measures satisfying linear PDE constraints (A. Arroyo-Rabasa, G. De Philippis, J. Hirsch, F. Rindler), Geom. Functions. Anal. (GAFA), to appear, Preprint.
  • Relaxation for partially coercive integral functionals with linear growth (F. Rindler, G. Shaw), Preprint.
  • On the two-state problem for general differential operators (G. De Philippis, L. Palmieri, F. Rindler), Nonlinear Anal. 177 (2018), 387-396, Online version, Preprint.
  • On the structure of measures constrained by linear PDEs (G. De Philippis, F. Rindler), Proc. ICM 2018, Preprint.
  • Liftings, Young measures, and lower semicontinuity (F. Rindler, G. Shaw), to appear in Arch. Ration. Mech. Anal, Online version (Open access).

Background publications

  • Regularity and approximation of strong solutions to rate-independent systems (F. Rindler, S. Schwarzacher, E. Süli), Math. Models Methods Appl. Sci. (M3AS) 27 (2017), 2511-2556, Online version, Preprint.
  • Lower semicontinuity and relaxation of linear-growth integral functionals under PDE constraints (A. Arroyo-Rabasa, G. De Philippis, F. Rindler), to appear in Adv. Calc. Var., Online version, Preprint.
  • On a conjecture of Cheeger (G. De Philippis, A. Marchese, F. Rindler), “Measure Theory in Non-Smooth Spaces” (Nicola Gigli, ed.), 2017, De Gruyter, Online version (Open Access).
  • Characterization of generalized Young measures generated by symmetric gradients (G. De Philippis, F. Rindler), Arch. Ration. Mech. Anal. 224 (2017) 1087-1125, Online version.
  • On the structure of A-free measures and applications (G. De Philippis, F. Rindler), Ann. of Math. 184 (2016), 1017-1039, Online version.
  • Directional oscillations, concentrations, and compensated compactness via microlocal compactness forms (F. Rindler), Arch. Ration. Mech. Anal. 215 (2015), 1-63. Online version.
  • Characterization of generalized gradient Young measures in W1,1 and BV (J. Kristensen, F. Rindler), Arch. Ration. Mech. Anal. 197 (2010), 539-598. Online version.