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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 ...
Uniform profile near the point defect of Landau-de Gennes model
(2022-11-04)
For the Landau-de Gennes functional on 3D domains,
$$
I_\varepsilon(Q,\Omega):=\int_{\Omega}\left\{\frac12|\nabla Q|^2+\frac{1}{\varepsilon^2}\left( -\frac{a^2}{2}\mathrm{tr}(Q^2)-\frac{b^2}{3}\mathrm{tr}(Q^3)+\frac{c^ ...
On the advection-diffusion equation with rough coefficients: Weak solutions and vanishing viscosity
(2022-11-01)
We deal with the vanishing viscosity scheme for the transport/continuity equation ∂tu+div(ub)=0 drifted by a divergence-free vector field b. Under general Sobolev assumptions on b, we show the convergence of such scheme ...
A unified approach towards the impossibility of finite time vanishing depth for incompressible free boundary flows
(2022-10-19)
In this paper we study the motion of an internal water wave and an internal wave in a porous medium. For these problems we establish that, if the free boundary and, in the case of the Euler equations, also the tangential ...
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 ...
Asymptotic behavior of the interface for entire vector minimizers in phase transitions
(2022-09-15)
We study globally bounded entire minimizers $u:\mathbb{R}^n\rightarrow\mathbb{R}^m$ of Allen-Cahn systems for potentials $W\geq 0$ with $\{W=0\}=\{a_1,...,a_N\}$ and $W(u)\sim |u-a_i|^\alpha$ near $u=a_i$, $0<\alpha<2$. ...
Sawyer-type inequalities for Lorentz spaces
(2022-06)
The Hardy-Littlewood maximal operator M satisfies the classical Sawyer-type estimate ∥Mfv∥L1,∞(uv)≤Cu,v‖f‖L1(u),where u∈ A1 and uv∈ A∞. We prove a novel extension of this result to the general restricted weak type case. ...
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 ...