32 citations · 242 across the 23 of their papers we have counts for
7 papers · 1 filter
A simple construction of potential operators for compensated compactness
Bogdan Raiţă
We give a short proof of the fact that each homogeneous linear differential operator of constant rank admits a homogeneous potential operator , meaning that $\ker A(x)=\math…
Concentration effects of BV gradients have gradient structure
Jan Kristensen, Bogdan Raiţă
We prove that the concentration effects arising from weakly-* convergent sequences of gradients of maps of bounded variation have gradient structure. This is in stark contrast with…
Bilevel training schemes in imaging for total-variation-type functionals with convex integrands
Valerio Pagliari, Kostas Papafitsoros, Bogdan Raiţă +1
In the context of image processing, given a -th order, homogeneous and linear differential operator with constant coefficients, we study a class of variational problems whose re…
Syzygies, constant rank, and beyond
Marc Härkönen, Lisa Nicklasson, Bogdan Raiţă
We study linear PDE with constant coefficients. The constant rank condition on a system of linear PDEs with constant coefficients is often used in the theory of compensated compact…
Compensation phenomena for concentration effects via nonlinear elliptic estimates
André Guerra, Bogdan Raiţă, Matthew Schrecker
We study compensation phenomena for fields satisfying both a pointwise and a linear differential constraint. This effect takes the form of nonlinear elliptic estimates, where const…
A trace inequality for solenoidal charges
Bogdan Raita, Daniel Spector, Dmitriy Stolyarov
We prove that for , one has the trace inequality \begin{align*} \int_{\mathbb{R}^d} |I_αF| \;dν\leq C |F|(\mathbb{R}^d)\|ν\|_{\mathcal{M}^{d-α}(\mathbb{R}^d)} \end{al…
Endpoint estimates for Hodge systems
Felipe Hernandez, Bogdan Raita, Daniel Spector
In this paper we give a simple proof of the endpoint Besov-Lorentz estimate $$ \|I_αF\|_{\dot{B}^{0,1}_{d/(d-α),1}(\mathbb{R}^d;\mathbb{R}^k)} \leq C \|F \|_{L^1(\mathbb{R}^d;\math…