Browsing Analysis of Partial Differential Equations (APDE) by Title
Now showing items 194213 of 266

Sawyertype inequalities for Lorentz spaces
(202206)The HardyLittlewood maximal operator M satisfies the classical Sawyertype 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 Scaling Limit from the Wave Map to the Heat Flow Into S2
(20190708)In this paper we study a limit connecting a scaled wave map with the heat flow into the unit sphere 𝕊2. We show quantitatively how the two equations are connected by means of an initial layer correction. This limit is ... 
Scattering with criticallysingular and δshell potentials
(2019)The authors consider a scattering problem for electric potentials that have a component which is critically singular in the sense of Lebesgue spaces, and a component given by a measure supported on a compact Lipschitz ... 
The Schrödinger equation and Uncertainty Principles
(202009)The main task of this thesis is the analysis of the initial data u0 of Schrödinger’s initial value problem in order to determine certain properties of its dynamical evolution. First we consider the elliptic Schrödinger ... 
SelfAdjoint Extensions for the Dirac Operator with CoulombType Spherically Symmetric Potentials
(2018)We describe the selfadjoint realizations of the operator $H:=i\alpha\cdot \nabla + m\beta + \mathbb V(x)$, for $m\in\mathbb R $, and $\mathbb V(x)= x^{1} ( \nu \mathbb{I}_4 +\mu \beta i \lambda \alpha\cdot{x}/{x}\,\beta)$, ... 
Selfadjointness of twodimensional Dirac operators on corner domains
(20210101)We investigate the selfadjointness of the twodimensional Dirac operator D, with quantumdot and Lorentzscalar ishell boundary conditions, on piecewise C2 domains (with finitely many corners). For both models, we prove ... 
Selfimproving PoincaréSobolev type functionals in product spaces
(2021)In this paper we give a geometric condition which ensures that (q, p)Poincar´eSobolev inequalities are implied from generalized (1, 1)Poincar´e inequalities related to L 1 norms in the context of product spaces. ... 
Selfsimilar dynamics for the modified Kortewegde Vries equation
(20190409)We prove a local well posedness result for the modified Kortewegde Vries equa tion in a critical space designed so that is contains selfsimilar solutions. As a consequence, we can study the flow of this equation around ... 
Sensitivity of twin boundary movement to sample orientation and magnetic field direction in NiMnGa
(2019)When applying a magnetic field parallel or perpendicular to the long edge of a parallelepiped Ni MnGa stick, twin boundaries move instantaneously or gradullay through the sample. We evaluate the sample shape dependence ... 
Sharp bounds for the ratio of modified Bessel functions
(20170621)Let $I_{\nu }\left( x\right) $ be the modified Bessel functions of the first kind of order $\nu $, and $S_{p,\nu }\left( x\right) =W_{\nu }\left( x\right) ^{2}2pW_{\nu }\left( x\right) x^{2}$ with $W_{\nu }\left( x\right) ... 
Sharp exponential localization for eigenfunctions of the Dirac Operator
(2018)We determine the fastest possible rate of exponential decay at infinity for eigenfunctions of the Dirac operator $\mathcal D_n + \mathbb V$, being $\mathcal D_n$ the massless Dirac operator in dimensions $n=2,3$ and ... 
Sharp local smoothing estimates for Fourier integral operators
(2019)The theory of Fourier integral operators is surveyed, with an emphasis on local smoothing estimates and their applications. After reviewing the classical background, we describe some recent work of the authors which ... 
A sharp lorentzinvariant strichartz norm expansion for the cubic wave equation in \mathbb{R}^{1+3}
(2020)We provide an asymptotic formula for the maximal Stri chartz norm of small solutions to the cubic wave equation in Minkowski space. The leading coefficient is given by Foschi’s sharp constant for the linear Strichartz ... 
Sharp reverse Hölder inequality for Cp weights and applications
(2020)We prove an appropriate sharp quantitative reverse Hölder inequality for the $C_p$ class of weights fromwhich we obtain as a limiting case the sharp reverse Hölder inequality for the $A_\infty$ class of weights (Hytönen ... 
Sharp weighted estimates involving one supremum
(201707)In this note, we study the sharp weighted estimate involving one supremum. In particular, we give a positive answer to an open question raised by Lerner and Moen. We also extend the result to rough homogeneous singular ... 
Shear flow dynamics in the BerisEdwards model of nematic liquid crystals
(20180214)We consider the BerisEdwards model describing nematic liquid crystal dynamics and restrict to a shear flow and spatially homogeneous situation. We analyze the dynamics focusing on the effect of the flow. We show that in ... 
Shell interactions for Dirac operators: On the point spectrum and the confinement
(20151231)Spectral properties and the confinement phenomenon for the coupling $H + V$ are studied, where $H =i\alpha \cdot \nabla + m\beta$ is the free Dirac operator in $\mathbb{R}^3$ and $V$ is a measurevalued potential. The ... 
Singular Perturbation of the Dirac Hamiltonian
(20171215)This thesis is devoted to the study of the Dirac Hamiltonian perturbed by deltatype potentials and Coulombtype potentials. We analysed the deltashell interaction on bounded and smooth domains and its approximation by ... 
Singularity formation for the 1D cubic NLS and the Schrödinger map on $\mathbb{S}^2$
(20170202)In this note we consider the 1D cubic Schrödinger equation with data given as small perturbations of a Dirac$\delta$ function and some other related equations. We first recall that although the problem for this type of ... 
Some geometric properties of Riemann’s nondifferentiable function
(20191106)Riemann’s nondifferentiable function is a celebrated example of a continuous but almost nowhere differentiable function. There is strong numeric evidence that one of its complex versions represents a geometric trajectory ...