32 citations · 242 across the 23 of their papers we have counts for
17 papers · 1 filter
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…
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…
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…
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 $$ \|I_αF\|_{\dot{B}^{0,1}_{d/(d-α),1}(\mathbb{R}^d;\mathbb{R}^k)} \leq C \|F \|_{L^1(\mathbb{R}^d;\math…
Compensated compactness: continuity in optimal weak topologies
André Guerra, Bogdan Raiţă, Matthew R. I. Schrecker
For -homogeneous linear differential operators of constant rank, we study the implication in and $\mathcal{A} v_j\rightarrow \mathcal{A}…
Oscillation and concentration in sequences of PDE constrained measures
Jan Kristensen, Bogdan Raiţă
We show that for constant rank partial differential operators , generalized Young measures generated by sequences of -free measures can be characterized b…
Quasiconvexity, null Lagrangians, and Hardy space integrability under constant rank constraints
André Guerra, Bogdan Raiţă
We present a systematic treatment of the theory of Compensated Compactness under Murat's constant rank assumption. We give a short proof of a sharp weak lower semicontinuity result…
A Note on Estimates for Elliptic Systems with Data
Bogdan Raiţă, Daniel Spector
In this paper we give necessary and sufficient conditions on the compatibility of a th order homogeneous linear elliptic differential operator and differential cons…
On limiting trace inequalities for vectorial differential operators
Franz Gmeineder, Bogdan Raita, Jean Van Schaftingen
We establish that trace inequalities $$\|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…
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…