We show that for constant rank partial differential operators A whose wave cones are
spanning, generalized Young measures generated by bounded sequences of A-free …

We introduce a general difference quotient representation for non-local operators
associated with a first-order linear operator. We establish new local to non-local estimates …

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 …

We establish higher integrability estimates for constant-coefficient systems of linear
PDEs\[\mathcal {A}\mu=\sigma,\] where $\mu\in\mathcal {M}(\Omega; V) $ and …

We give a simple and constructive extension of Rait, a's result that every constant-rank
operator possesses an exact potential and an exact annihilator. Our construction is …

We give a short proof of the fact that each homogeneous linear differential operator $ A $ of
constant rank admits a homogeneous potential operator $ B $, meaning that $\ker A …

Contrary to the incompressible case, not every measure-valued solution of the compressible
Euler equations can be generated by weak solutions or a vanishing viscosity sequence. In …

Let $1< p<\infty $ and let $\Omega $ be an open and bounded set of $\mathbb R^ n $. We
establish classical Korn inequalities\[\inf_ {\substack {v\in L^ p (\Omega)\\\mathcal A v= 0}} …

In this paper, we prove that for each closed differential form u∈ L 1 (RN;(RN)∗∧...∧(RN)∗),
which is almost in L∞ in the sense that∫{y∈ RN:| u (y)|≥ L}| u (y)| dy< ε for some L> 0 and …

Let B be a homogeneous differential operator of order l= 1 or l= 2. We show that a sequence
of functions of the form (B uj) j converging in the L 1-sense to a compact, convex set K can …