Browsing Analysis of Partial Differential Equations (APDE) by Title
Now showing items 4867 of 167

Flow with $A_\infty(\mathbb R)$ density and transport equation in $\mathrm{BMO}(\mathbb R)$
(Forum of Mathematics, Sigma, 201911)We show that, if $b\in L^1(0,T;L^1_{\rm {loc}}(\mathbb R))$ has spatial derivative in the JohnNirenberg space ${\rm{BMO}}(\mathbb R)$, then it generates a unique flow $\phi(t,\cdot)$ which has an $A_\infty(\mathbb R)$ ... 
Gaussian Decay of Harmonic Oscillators and related models
(Journal of Mathematical Analysis and Applications, 20170515)We prove that the decay of the eigenfunctions of harmonic oscillators, uniform electric or magnetic fields is not stable under 0order complex perturbations, even if bounded, of these Hamiltonians, in the sense that we can ... 
A geometric and physical study of Riemann's nondifferentiable function
(20200708)Riemann's nondifferentiable function is a classic example of a continuous but almost nowhere differentiable function, whose analytic regularity has been widely studied since it was proposed in the second half of the 19th ... 
Geometric differentiability of Riemann's nondifferentiable function
(Advances in Mathematics, 202006)Riemann’s nondifferentiable function is a classic example of a continuous function which is almost nowhere differentiable, and many results concerning its analytic regularity have been shown so far. However, it can also ... 
Global Uniqueness for The Calderón Problem with Lipschitz Conductivities
(Forum of Mathematics, Pi, 20160101)We prove uniqueness for the Calderón problem with Lipschitz conductivities in higher dimensions. Combined with the recent work of Haberman, who treated the three and fourdimensional cases, this confirms a conjecture of ... 
Global wellposedness and twistwave solutions for the inertial QianSheng model of liquid crystals
(Journal of Differential Equations, 20171002)We consider the inertial QianSheng model of liquid crystals which couples a hyperbolictype equation involving a secondorder material derivative with a forced incompressible NavierStokes system. We study the energy law ... 
A Global wellposedness result for the Rosensweig system of ferrofluids
(Rev. Mat. Iberoam., 2019)In this Paper we study a BlochTorrey regularization of the Rosensweig system for ferrofluids. The scope of this paper is twofold. First of all, we investigate the existence and uniqueness of LerayHopf solutions of this ... 
Hardy uncertainty principle, convexity and parabolic evolutions
(Communications in Mathematical Physics, 20160901)We give a new proof of the $L^2$ version of Hardy’s uncertainty principle based on calculus and on its dynamical version for the heat equation. The reasonings rely on new logconvexity properties and the derivation of ... 
Hardytype inequalities for fractional powers of the DunklHermite operator
(Proc. Edinburgh Math. Soc. (2), 2018)We prove Hardytype inequalities for a fractional Dunkl–Hermite operator, which incidentally gives Hardy inequalities for the fractional harmonic oscillator as well. The idea is to use hharmonic expansions to reduce the ... 
A Hardytype inequality and some spectral characterizations for the DiracCoulomb operator
(Revista Matemática Complutense, 20190702)We prove a sharp Hardytype inequality for the Dirac operator. We exploit this inequality to obtain spectral properties of the Dirac operator perturbed with Hermitian matrixvalued potentials V of Coulomb type: we characterise ... 
A Hardytype inequality and some spectral characterizations for the Dirac–Coulomb operator
(Revista Matemática Complutense, 201906)We prove a sharp Hardytype inequality for the Dirac operator. We exploit this inequality to obtain spectral properties of the Dirac operator perturbed with Hermitian matrixvalued potentials $\mathbf V$ of Coulomb type: ... 
HartreeFock theory with a selfgenerated magnetic field
(Journal of Mathematical Physics, 20170601)We prove the existence of a ground state within the HartreeFock theory for atoms and molecules, in the presence of selfgenerated magnetic fields, with and without direct spin coupling. The ground state exists provided ... 
Highly rotating fluids with vertical stratification for periodic data and vanishing vertical viscosity
(Revista Matemática Iberoamericana, 201707)We prove that the threedimensional, periodic primitive equations with zero vertical diffusivity are globally well posed if the Rossby and Froude number are sufficiently small. The initial data is considered to be of zero ... 
HölderLebesgue regularity and almost periodicity for semidiscrete equations with a fractional Laplacian
(Discrete Contin. Dyn. Syst., 2018)We study the equations $ \partial_t u(t,n) = L u(t,n) + f(u(t,n),n); \partial_t u(t,n) = iL u(t,n) + f(u(t,n),n)$ and $ \partial_{tt} u(t,n) =Lu(t,n) + f(u(t,n),n)$, where $n\in \mathbb{Z}$, $t\in (0,\infty)$, and $L$ ... 
Hypocoercivity of linear kinetic equations via Harris's Theorem
(Kinetic & Related Models, 20190227)We study convergence to equilibrium of the linear relaxation Boltzmann (also known as linear BGK) and the linear Boltzmann equations either on the torus $(x,v) \in \mathbb{T}^d \times \mathbb{R}^d$ or on the whole ... 
Improved A1 − A∞ and related estimates for commutators of rough singular integrals
(Proceedings of the Edinburgh Mathematical Society, 2017)An $A_1A_\infty$ estimate improving a previous result in [22] for $[b, T_\Omega]$ with $\Omega\in L^\infty(S^{n1})$ and $b\in BMO$ is obtained. Also a new result in terms of the $A_\infty$ constant and the one ... 
Improved fractional Poincaré type inequalities in John domains
(Arkiv för Matematik, 2019)We obtain improved fractional Poincaré inequalities in John domains of a metric space $(X, d)$ endowed with a doubling measure $\mu$ under some mild regularity conditions on the measure $\mu$. We also give sufficient ... 
Inverse scattering for a random potential
(201605)In this paper we consider an inverse problem for the $n$dimensional random Schrödinger equation $(\Deltaq+k^2)u = 0$. We study the scattering of plane waves in the presence of a potential $q$ which is assumed to be a ... 
Klein's Paradox and the Relativistic $\delta$shell Interaction in $\mathbb{R}^3$
(Analysis & PDE, 201711)Under certain hypothesis of smallness of the regular potential $\mathbf{V}$, we prove that the Dirac operator in $\mathbb{R}^3$ coupled with a suitable rescaling of $\mathbf{V}$, converges in the strong resolvent sense ... 
Landaude Gennes Corrections to the OseenFrank Theory of Nematic Liquid Crystals
(Archive for Rational Mechanics and Analysis, 20200103)We study the asymptotic behavior of the minimisers of the Landaude Gennes model for nematic liquid crystals in a twodimensional domain in the regime of small elastic constant. At leading order in the elasticity constant, ...