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 …

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 introduce a new space of generalized functions of bounded deformation $ GBD_ {F} $,
made of functions u whose one-dimensional slice $ u (\gamma)\cdot\dot {\gamma} $ has …

We study the $ L^ 2$-gradient flows for functionals of the type $\int_ {\Omega} f (x,\mathbb
{A} u)\,\mathrm {dx} $, where $ f $ is a convex function of linear growth and $\mathbb {A} $ is …

In this paper a novel criterion for the slicing of the jump set of a function is provided, which
bypasses the codimension-one and the parallelogram law techniques developed in $ BD …

In this paper we introduce a new class of integralgeometric measures in $\mathbb {R}^ n $,
built upon the idea of slicing, and depending on the dimension $0\leq m\leq n $ and on the …

We study sharpness of various generalizations of Frostman's lemma. These generalizations
provide better estimates for the lower Hausdorff dimension of measures. As a corollary, we …