Browsing Analysis of Partial Differential Equations (APDE) by Issue Date
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Three Observations on Commutators of Singular Integral Operators with BMO Functions
(20160701)Three observations on commutators of Singular Integral Operators with BMO functions are exposed, namely 1  The already known subgaussian local decay for the commutator, namely $\[\frac{1}{Q}\left\left\{x\in Q\, : ... 
Borderline Weighted Estimates for Commutators of Singular Integrals
(20160701)In this paper we establish the following estimate \[ w\left(\left\{ x\in\mathbb{R}^{n}\,:\,\left[b,T]f(x)\right > \lambda\right\} \right)\leq \frac{c_{T}}{\varepsilon^{2}}\int_{\mathbb{R}^{n}}\Phi\left(\b\_{BMO}\f ... 
A note on the offdiagonal MuckenhouptWheeden conjecture
(20160701)We obtain the offdiagonal MuckenhouptWheeden conjecture for CalderónZygmund operators. Namely, given $1 < p < q < \infty$ and a pair of weights $(u; v)$, if the HardyLittlewood maximal function satisfies the following ... 
$A_1$ theory of weights for rough homogeneous singular integrals and commutators
(20160701)Quantitative $A_1A_\infty$ estimates for rough homogeneous singular integrals $T_{\Omega}$ and commutators of $BMO$ symbols and $T_{\Omega}$ are obtained. In particular the following estimates are proved: \[ \T_\Omega ... 
Spectral Transitions for AharonovBohm Laplacians on Conical Layers
(20160711)We consider the Laplace operator in a tubular neighbourhood of a conical surface of revolution, subject to an AharonovBohm magnetic field supported on the axis of symmetry and Dirichlet boundary conditions on the boundary ... 
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 ... 
Uniqueness and Properties of Distributional Solutions of Nonlocal Equations of Porous Medium Type
(20160901)We study the uniqueness, existence, and properties of bounded distributional solutions of the initial value problem for the anomalous diffusion equation $\partial_tu\mathcal{L}^\mu [\varphi (u)]=0$. Here $\mathcal{L}^\mu$ ... 
Optimal control of the Lotka–Volterra system: turnpike property and numerical simulations
(20160901)The LotkaVolterra model is a differential system of two coupled equations representing the interaction of two species: a prey one and a predator one. We formulate an optimal control problem adding the effect of hunting ... 
On sums involving Fourier coefficients of Maass forms for SL(3,Z)
(20160910)We derive a truncated Voronoi identity for rationally additively twisted sums of Fourier coefficients of Maass forms for SL(3,Z), and as an application obtain a pointwise estimate and a second moment estimate for the sums ... 
Reconstruction from boundary measurements for less regular conductivities
(20161001)In this paper, following Nachman's idea [14] and Haberman and Tataru's idea [9], we reconstruct $C^1$ conductivity $\gamma$ or Lipchitz conductivity $\gamma$ with small enough value of $\nabla log\gamma$ in a Lipschitz ... 
New bounds for bilinear CalderónZygmund operators and applications
(20161125)In this work we extend Lacey’s domination theorem to prove the pointwise control of bilinear Calderón–Zygmund operators with Dini–continuous kernel by sparse operators. The precise bounds are carefully tracked following ... 
On the controllability of Partial Differential Equations involving nonlocal terms and singular potentials
(20161212)In this thesis, we investigate controllability and observability properties of Partial Differential Equations describing various phenomena appearing in several fields of the applied sciences such as elasticity theory, ... 
Dimension reduction for the micromagnetic energy functional on curved thin films
(20161214)Micromagnetic con gurations of the vortex and onion type have beenwidely studied in the context of planar structures. Recently a signi cant interest to micromagnetic curved thin lms has appeared. In particular, thin ... 
A strategy for selfadjointness of Dirac operators: Applications to the MIT bag model and deltashell interactions
(20161221)We develop an approach to prove selfadjointness of Dirac operators with boundary or transmission conditions at a $C^2$compact surface without boundary. To do so we are lead to study the layer potential induced by the ... 
Liquid crystal defects in the Landau–de Gennes theory in two dimensions — Beyond the oneconstant approximation
(20161231)We consider the twodimensional Landaude Gennes energy with several elastic constants, subject to general $k$radially symmetric boundary conditions. We show that for generic elastic constants the critical points consistent ... 
Lorentz estimates for the gradient of weak solutions to elliptic obstacle problems with partially BMO coefficients
(2017)We prove global Lorentz estimates for variable power of the gradient of weak solution to linear elliptic obstacle problems with small partially BMO coefficients over a bounded nonsmooth domain. Here, we assume that the ... 
Spectral asymptotics for $\delta$interactions on sharp cones
(2017)We investigate the spectrum of threedimensional Schr\"odinger operators with $\delta$interactions of constant strength supported on circular cones. As shown in earlier works, such operators have infinitely many eigenvalues ... 
Mixed norm estimates for the Cesàro means associated with DunklHermite expansions
(2017)Our main goal in this article is to study mixed norm estimates for the Cesàro means associated with DunklHermite expansions on $\mathbb{R}^d$. These expansions arise when one considers the DunklHermite operator ... 
On pointwise and weighted estimates for commutators of CalderónZygmund operators
(2017)In recent years, it has been well understood that a CalderónZygmund operator T is pointwise controlled by a finite number of dyadic operators of a very simple structure (called the sparse operators). We obtain a similar ... 
A characterization of two weight norm inequality for LittlewoodPaley $g_{\lambda}^{*}$function
(2017)Let $n\ge 2$ and $g_{\lambda}^{*}$ be the wellknown high dimensional LittlewoodPaley function which was defined and studied by E. M. Stein, $$g_{\lambda}^{*}(f)(x)=\bigg(\iint_{\mathbb R^{n+1}_{+}} \Big(\frac{t}{t+xy ...