39 citations · 76 across the 27 of their papers we have counts for
37 papers
Scale-invariant bounds on thin sets for measures satisfying a first-order PDE and the anisotropic Michael-Simon inequality
Guido De Philippis, Luca Gennaioli, Alessandro Pigati +1
We prove mass estimates for PDE-constrained measures on sets of -finite -measure, assuming an appropriate rank condition. As an application, we derive a Michael-…
Shape optimization of light structures with general Hooke's laws
Dimitrios Andreakis, Flaviana Iurlano, Filip Rindler
For the minimum-compliance shape optimization problem it was established recently [\textit{Duke Math.\ J.} 172 (2023), 43--103] that a sequence of approximately optimal shapes of e…
Concentration phenomena and the Vanishing Mass Conjecture
Luca Gennaioli, Filip Rindler
Concentrating (that is, non-equi-integrable) sequences of functions satisfying linear PDE constraints arise in a wide variety of problems in PDE, the calculus of variations, and ge…
Existence and uniqueness for the transport of currents by Lipschitz vector fields
Paolo Bonicatto, Giacomo Del Nin, Filip Rindler
This work establishes the existence and uniqueness of solutions to the initial-value problem for the geometric transport equation $$ \frac{\mathrm{d}}{\mathrm{d} t}T_t+\mathcal{L}_…
On the converse of Pansu's Theorem
Guido De Philippis, Andrea Marchese, Andrea Merlo +2
We provide a suitable generalisation of Pansu's differentiability theorem to general Radon measures on Carnot groups and we show that if Lipschitz maps between Carnot groups are Pa…
Transport of currents and geometric Rademacher-type theorems
Paolo Bonicatto, Giacomo Del Nin, Filip Rindler
The transport of many kinds of singular structures in a medium, such as vortex points/lines/sheets in fluids, dislocation loops in crystalline plastic solids, or topological singul…
Energetic solutions to rate-independent large-strain elasto-plastic evolutions driven by discrete dislocation flow
Filip Rindler
This work rigorously implements a recent model of large-strain elasto-plastic evolution in single crystals where the plastic flow is driven by the movement of discrete dislocation…
Space-time integral currents of bounded variation
Filip Rindler
Motivated by a recent model for elasto-plastic evolutions that are driven by the flow of dislocations, this work develops a theory of space-time integral currents with bounded vari…
Elasto-plastic evolution of single crystals driven by dislocation flow
Thomas Hudson, Filip Rindler
This work introduces a model for large-strain, geometrically nonlinear elasto-plastic dynamics in single crystals. The key feature of our model is that the plastic dynamics are ent…
Higher integrability for measures satisfying a PDE constraint
Adolfo Arroyo-Rabasa, Guido De Philippis, Jonas Hirsch +2
We establish higher integrability estimates for constant-coefficient systems of linear PDEs \[ \mathcal{A} μ= σ, \] where and are ve…
Shape optimization of light structures and the vanishing mass conjecture
Jean-Francois Babadjian, Flaviana Iurlano, Filip Rindler
This work proves rigorous results about the vanishing-mass limit of the classical problem to find a shape with minimal elastic compliance. Contrary to all previous results in the m…
Probabilistic solution of chaotic dynamical system inverse problems using Bayesian Artificial Neural Networks
David K. E. Green, Filip Rindler
This paper demonstrates the application of Bayesian Artificial Neural Networks to Ordinary Differential Equation (ODE) inverse problems. We consider the case of estimating an unkno…
Fine properties of functions of bounded deformation -- an approach via linear PDEs
Guido De Philippis, Filip Rindler
In this survey we collect some recent results obtained by the authors and collaborators concerning the fine structure of functions of bounded deformation (BD). These maps are $\mat…
Model inference for Ordinary Differential Equations by parametric polynomial kernel regression
David K. E. Green, Filip Rindler
Model inference for dynamical systems aims to estimate the future behaviour of a system from observations. Purely model-free statistical methods, such as Artificial Neural Networks…
Two-speed solutions to non-convex rate-independent systems
Filip Rindler, Sebastian Schwarzacher, Juan J. L. Velazquez
We consider evolutionary PDE inclusions of the form \[ -λ\dot{u}_λ+ Δu - \mathrm{D} W_0(u) + f \ni \partial \mathcal{R}_1(\dot{u}) \qquad\text{in ,} \] where $\math…
Concentration versus oscillation effects in brittle damage
Jean-Francois Babadjian, Flaviana Iurlano, Filip Rindler
This work is concerned with an asymptotic analysis, in the sense of -convergence, of a sequence of variational models of brittle damage in the context of linearized elasticity.…
On the relaxation of integral functionals depending on the symmetrized gradient
Kamil Kosiba, Filip Rindler
We prove results on the relaxation and weak* lower semicontinuity of integral functionals of the form \[ \mathcal{F}[u] := \int_Ω f \bigg( \frac{1}{2} \bigl( \nabla u(x) + \nabla u…
Dimensional estimates and rectifiability for measures satisfying linear PDE constraints
Adolfo Arroyo-Rabasa, Guido De Philippis, Jonas Hirsch +1
We establish the rectifiability of measures satisfying a linear PDE constraint. The obtained rectifiability dimensions are optimal for many usual PDE operators, including all first…
Relaxation for partially coercive integral functionals with linear growth
Filip Rindler, Giles Shaw
We prove an integral representation theorem for the -relaxation of the functional \[ \mathcal{F}\colon u\mapsto\int_Ωf(x,u(x),\nabla u(x))\;\mathrm{dd…
On the two-state problem for general differential operators
Guido De Philippis, Luca Palmieri, Filip Rindler
In this note we generalize the Ball-James rigidity theorem for gradient differential inclusions to the setting of a general linear differential constraint. In particular, we prove…
On the structure of measures constrained by linear PDEs
Guido De Philippis, Filip Rindler
The aim of this note is to present some recent results on the structure of the singular part of measures satisfying a PDE constraint and to describe some applications.
Liftings, Young measures, and lower semicontinuity
Giles Shaw, Filip Rindler
This work introduces liftings and their associated Young measures as new tools to study the asymptotic behaviour of sequences of pairs for $(u_j)_j \in \mathrm{BV}(Ω;…
Regularity and approximation of strong solutions to rate-independent systems
Filip Rindler, Sebastian Schwarzacher, Endre Süli
Rate-independent systems arise in a number of applications. Usually, weak solutions to such problems with potentially very low regularity are considered, requiring mathematical tec…
Lower semicontinuity and relaxation of linear-growth integral functionals under PDE constraints
Adolfo Arroyo-Rabasa, Guido De Philippis, Filip Rindler
We show general lower semicontinuity and relaxation theorems for linear-growth integral functionals defined on vector measures that satisfy linear PDE side constraints (of arbitrar…