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Now showing items 1-10 of 248

#### On the Calderón problem for nonlocal Schrödinger equations with homogeneous, directionally antilocal principal symbols

(2022-12-25)

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 ...

#### Motion of a rigid body in a compressible fluid with Navier-slip boundary condition

(2022-11-25)

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 ...

#### Kato–Ponce estimates for fractional sublaplacians in the Heisenberg group

(2022-11-04)

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 ...

#### Various results concerning homogenisation of nematic liquid crystals

(2022-10-17)

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 ...

#### A∞ condition for general bases revisited: complete classification of definitions

(2022-05-27)

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 ...

#### Maximal operators on the infinite-dimensional torus

(2022-03-31)

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 ...

#### Hölder regularity and convergence for a non-local model of nematic liquid crystals in the large-domain limit

(2022-02-01)

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 ...

#### The Two Dimensional Liquid Crystal Droplet Problem with Tangential Boundary Condition

(2022-01-18)

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

(2022-01-05)

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 ...

#### Existence of a weak solution to a nonlinear fluid-structure interaction problem with heat exchange

(2022-01-01)

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 ...