We establish a general structure theorem for the singular part of 𝓐-free Radon measures,
where 𝓐 is a linear PDE operator. By applying the theorem to suitably chosen differential …

In 1989, Burnett conjectured that, under appropriate assumptions, the limit of highly
oscillatory solutions to the Einstein vacuum equations is a solution of the Einstein–massless …

We consider a dynamic capillarity equation with stochastic forcing on a compact
Riemannian manifold $(M, g) $:\begin {equation*} d\left (u_ {\varepsilon,\delta}-\delta\Delta …

Can every measure-valued solution to the compressible Euler equations be approximated
by a sequence of weak solutions? We prove that the answer is negative: generalizing a well …

In this article, we introduced a new measure termed as Q-measure to represent a weak* limit
of the barycenter of a sequence of Borel measurable function. The Q-measure is defined by …

Microlocal defect functionals (H-measures, H-distributions, semiclassical measures etc.) are
objects which determine, in some sense, the lack of strong compactness for weakly …

H-distributions associated with weakly convergent sequences in Sobolev spaces are
determined. It is shown that a weakly convergent sequence (u_n)(un) in W^-k, p (R^ d) Wk, p …

We consider a homogeneous differential operator A and show an improved version of
Murat's condition for A-quasiaffine functions, provided that the operator A satisfies the …

This study investigates the $ L^ 1_ {\operatorname {loc}} $ compactness of velocity averages
of sequences of solutions $\{u_n\} $ for a class of kinetic equations. The equations are …

What does it mean to study PDE (= Partial Differential Equation)? How and what to do" to
claim proudly that I'm studying a certain PDE"? Newton mechanic uses mainly ODE …