In this article we consider direct and inverse problems for α-stable, elliptic nonlocal operators whose kernels are possibly only supported on cones and which satisfy the structural condition of directional antilocality ...

In this work, we study the motion of a rigid body in a bounded domain which is filled with a compressible isentropic fluid. We consider the Navier-slip boundary condition at the interface as well as at the boundary of the ...

We give a proof of commutator estimates for fractional powers of the sublaplacian on the Heisenberg group. Our approach is based on pointwise and $L^p$ estimates involving square fractional integrals and Littlewood--Paley ...

In this thesis we present various results concerning homogenisation of nematic liquid crystals: two of them are in perforated domains, while the other one concerns rates of convergence for boundary homogenisation. The first ...

We refer to the discussion on different characterizations of the A∞ class of weights, initiated by Duoandikoetxea, Martín-Reyes, and Ombrosi [Math. Z. 282 (2016), pp. 955–972]. Twelve definitions of the A∞ condition ...

We study maximal operators related to bases on the infinite-dimensional torus $\tom$. {For the normalized Haar measure $dx$ on $\mathbb{T}^\omega$ it is known that $M^{\mathcal{R}_0}$, the maximal operator associated with ...

We consider a non-local free energy functional, modelling a competition between entropy and pairwise interactions reminiscent of the second order virial expansion, with applications to nematic liquid crystals as a particular ...

This paper studies a shape optimization problem which reduces to a nonlocal free boundary problem involving perimeter. It is motivated by a study of liquid crystal droplets with a tangential anchoring boundary condition ...

Rotational smoothing is a phenomenon consisting in a gain of regularity by means of averaging over rotations. This phenomenon is present in operators that regularize only in certain directions, in contrast to operators ...

In this paper, we study a nonlinear interaction problem between a thermoelastic shell and a heat-conducting fluid. The shell is governed by linear thermoelasticity equations and encompasses a time-dependent domain which ...