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Correlation imaging in inverse scattering is tomography on probability distributions
(2018-12-04)
Scattering from a non-smooth random field on the time domain is studied for plane waves that propagate simultaneously through the potential in variable angles. We first derive sufficient conditions for stochastic moments ...
Regularity of maximal functions on Hardy–Sobolev spaces
(2018-12-01)
We prove that maximal operators of convolution type associated to smooth kernels are bounded in the homogeneous Hardy–Sobolev spaces H1,p(Rd) when p > d/(d + 1). This range of exponents is sharp. As a by-product of the ...
Unique determination of the electric potential in the presence of a fixed magnetic potential in the plane
(2018-12)
For electric and magnetic potentials with compact support, we consider the magnetic Schrödinger equation with fixed positive energy. Under a mild additional regularity hypothesis, and with fixed magnetic potential, we show ...
Determination of convection terms and quasi-linearities appearing in diffusion equations
(2018-12)
We consider the highly nonlinear and ill posed inverse problem of determining some general expression appearing in the a diffusion equation from measurements of solutions on the lateral boundary. We consider both linear ...
Some remark on the existence of infinitely many nonphysical solutions to the incompressible Navier-Stokes equations
(2018-10)
We prove that there exist infinitely many distributional solutions with infinite kinetic energy to both the incompressible Navier-Stokes equations in $ \mathbb{R}^2 $ and Burgers equation in $\mathbb{R} $ with vanishing ...
On the global well-posedness of a class of 2D solutions for the Rosensweig system of ferrofluids
(2018-09)
We study a class of 2D solutions of a Bloch-Torrey regularization of the Rosensweig system in the whole space, which arise when the initial data and the external magnetic field are 2D. We prove that such solutions are ...
Uniqueness of degree-one Ginzburg–Landau vortex in the unit ball in dimensions N ≥ 7
(2018-09-01)
For ε>0, we consider the Ginzburg-Landau functional for RN-valued maps defined in the unit ball BN⊂RN with the vortex boundary data x on ∂BN. In dimensions N≥7, we prove that for every ε>0, there exists a unique global ...
Vector-valued operators, optimal weighted estimates and the $C_p$ condition
(2018-09)
In this paper some new results concerning the $C_p$ classes introduced by Muckenhoupt and later extended by Sawyer, are provided. In particular we extend the result to the full range expected $p>0$, to the weak norm, to ...
Proof of an extension of E. Sawyer's conjecture about weighted mixed weak-type estimates
(2018-09)
We show that if $v\in A_\infty$ and $u\in A_1$, then there is a constant $c$ depending on the $A_1$ constant of $u$ and the $A_{\infty}$ constant of $v$ such that
$$\Big\|\frac{ T(fv)} {v}\Big\|_{L^{1,\infty}(uv)}\le c\, ...
Weighted norm inequalities for rough singular integral operators
(2018-08-17)
In this paper we provide weighted estimates for rough operators, including rough homogeneous singular integrals $T_\Omega$ with $\Omega\in L^\infty(\mathbb{S}^{n-1})$ and the Bochner--Riesz multiplier at the critical index ...