Browsing Analysis of Partial Differential Equations (APDE) by Title
Now showing items 7190 of 240

Flow with $A_\infty(\mathbb R)$ density and transport equation in $\mathrm{BMO}(\mathbb R)$
(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 $A_\infty(\mathbb R)$ ... 
The Frisch–Parisi formalism for fluctuations of the Schrödinger equation
(2022)We consider the solution of the Schrödinger equation $u$ in $\mathbb{R}$ when the initial datum tends to the Dirac comb. Let $h_{\text{p}, \delta}(t)$ be the fluctuations in time of $\int\lvert x \rvert^{2\delta}\lvert ... 
Gaussian Decay of Harmonic Oscillators and related models
(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 ... 
Generalized PoincaréSobolev inequalities
(202012)PoincaréSobolev inequalities are very powerful tools in mathematical analysis which have been extensively used for the study of differential equations and their validity is intimately related with the geometry of the ... 
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
(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 ... 
Geometric Harmonic Analysis
(2021)This thesis is the compilation of the results obtained during my PhD, which started in January 2018 and is being completed in the end of 2021. The main matter is divided into ve chapters, Chapters 2 6. Each of these ... 
Global Uniqueness for The Calderón Problem with Lipschitz Conductivities
(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
(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
(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
(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
(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
(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
(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: ... 
A Hardytype inequality and some spectral characterizations for the Dirac–Coulomb operator
(20200101)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 ... 
HartreeFock theory with a selfgenerated magnetic field
(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
(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 ... 
Hölder regularity and convergence for a nonlocal model of nematic liquid crystals in the largedomain limit
(20220201)We consider a nonlocal 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 ... 
HölderLebesgue regularity and almost periodicity for semidiscrete equations with a fractional Laplacian
(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
(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 ...