32 citations · 242 across the 23 of their papers we have counts for
23 papers
Gaussian Process Priors for Systems of Linear Partial Differential Equations with Constant Coefficients
Marc Härkönen, Markus Lange-Hegermann, Bogdan Raiţă
Partial differential equations (PDEs) are important tools to model physical systems and including them into machine learning models is an important way of incorporating physical kn…
Boundary ellipticity and limiting -estimates on halfspaces
Franz Gmeineder, Bogdan Raiţă, Jean Van Schaftingen
We identify necessary and sufficient conditions on th order differential operators in terms of a fixed halfspace such that the Gagliardo--N…
On Scaling Properties for Two-State Problems and for a Singularly Perturbed Structure
Bodgan Raiţă, Angkana Rüland, Camillo Tissot
In this article we study quantitative rigidity properties for the compatible and incompatible two-state problems for suitable classes of -free operators and for a sing…
Weak and Strong Extremal Biquadratics
Grigoriy Blekherman, Bogdan Raiţă, Isabelle Shankar +1
We study quasiconvex quadratic forms on matrices which correspond to nonnegative biquadratic forms in variables. We disprove a conjecture stated by Harutyunyan…
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 $$ \|I_αF\|_{\dot{B}^{0,1}_{d/(d-α),1}(\mathbb{R}^d;\mathbb{R}^k)} \leq C \|F \|_{L^1(\mathbb{R}^d;\math…
Compensated compactness: continuity in optimal weak topologies
André Guerra, Bogdan Raiţă, Matthew R. I. Schrecker
For -homogeneous linear differential operators of constant rank, we study the implication in and $\mathcal{A} v_j\rightarrow \mathcal{A}…
On the necessity of the constant rank condition for estimates
André Guerra, Bogdan Raiţă
We consider a generalization of the elliptic -estimate suited for linear operators with non-trivial kernels. A classical result of Schulenberger and Wilcox (Ann. Mat. Pura App…
Oscillation and concentration in sequences of PDE constrained measures
Jan Kristensen, Bogdan Raiţă
We show that for constant rank partial differential operators , generalized Young measures generated by sequences of -free measures can be characterized b…
Quasiconvexity, null Lagrangians, and Hardy space integrability under constant rank constraints
André Guerra, Bogdan Raiţă
We present a systematic treatment of the theory of Compensated Compactness under Murat's constant rank assumption. We give a short proof of a sharp weak lower semicontinuity result…
A Note on Estimates for Elliptic Systems with Data
Bogdan Raiţă, Daniel Spector
In this paper we give necessary and sufficient conditions on the compatibility of a th order homogeneous linear elliptic differential operator and differential cons…
On limiting trace inequalities for vectorial differential operators
Franz Gmeineder, Bogdan Raita, Jean Van Schaftingen
We establish that trace inequalities $$\|D^{k-1}u\|_{L^{\frac{n-s}{n-1}}(\mathbb{R}^{n},dμ)} \leq c \|μ\|_{L^{1,n-s}(\mathbb{R}^{n})}^{\frac{n-1}{n-s}}\|\mathbb{A}[D]u\|_{L^{1}(\ma…
Continuity and canceling operators of order on
Bogdan Raiţă, Anna Skorobogatova
We prove that for elliptic and canceling linear differential operators of order on , continuity of a map can be inferred from the fact that $\mat…
-estimates for constant rank operators
Bogdan Raiţă
We show that the inequality holds for vector fields $u\in\mathrm{…
Potentials for -quasiconvexity
Bogdan Raita
We show that each constant rank operator admits an exact potential in frequency space. We use this fact to show that the notion of -quasicon…
On critical -differentiability of -maps
Franz Gmeineder, Bogdan Raita
We prove that functions of locally bounded deformation on are -differentiable almost everywhere. More generally, we show that this critical $\m…
Critical -differentiability of -maps and canceling operators
Bogdan Raiţă
We give a generalization of Dorronsoro's Theorem on critical -Taylor expansions for -maps on , i.e., we characterize homogeneous linear d…
Embeddings for -weakly differentiable functions on domains
Franz Gmeineder, Bogdan Raiţă
We prove that the critical embedding holds if and only if the -homogeneous, linear differential oper…