Analysis of Partial Differential Equations (APDE): Recent submissions
Now showing items 120 of 120

On extension problem, trace hardy and Hardy’s inequalities for some fractional Laplacians
(Communications on pure and applied analysis, 201909)We obtain generalised trace Hardy inequalities for fractional powers of general operators given by sums of squares of vector fields. Such inequalities are derived by means of particular solutions of an extended equation ... 
Bloom type upper bounds in the product BMO setting
(Journal of Geometric Analysis, 20190408)We prove some Bloom type estimates in the product BMO setting. More specifically, for a bounded singular integral $T_n$ in $\mathbb R^n$ and a bounded singular integral $T_m$ in $\mathbb R^m$ we prove that $$ \ [T_n^1, ... 
Convex Integration Arising in the Modelling of ShapeMemory Alloys: Some Remarks on Rigidity, Flexibility and Some Numerical Implementations
(Journal of Nonlinear Science, 20190330)We study convex integration solutions in the context of the modelling of shapememory alloys. The purpose of the article is twofold, treating both rigidity and flexibility prop erties: Firstly, we relate the maximal ... 
Topological singular set of vectorvalued maps, I: application to manifoldconstrained Sobolev and BV spaces
(Calculus of Variations and Partial Differential Equations, 20190330)We introduce an operator $\mathbf{S}$ on vectorvalued maps $u$ which has the ability to capture the relevant topological information carried by $u$. In particular, this operator is defined on maps that take values in a ... 
Order Reconstruction for neatics on squares with isotropic inclusions: A Landaude Gennes study
(SIAM Journal on Applied Mathematics, 20190330)e study a modified Landaude Gennes model for nematic liq uid crystals, where the elastic term is assumed to be of subquadratic growth in the gradient. We analyze the behaviour of global minimizers in two and threedimensional ... 
Bloom type inequality for biparameter singular integrals: efficient proof and iterated commutators
(International Mathematics Research Notices, 20190314)Utilising some recent ideas from our bilinear biparameter theory, we give an efficient proof of a twoweight Bloom type inequality for iterated commutators of linear biparameter singular integrals. We prove that if $T$ ... 
Boundary Triples for the Dirac Operator with CoulombType Spherically Symmetric Perturbations
(Journal of Mathematical Physics, 201902)We determine explicitly a boundary triple for the Dirac operator $H:=i\alpha\cdot \nabla + m\beta + \mathbb V(x)$ in $\mathbb R^3$, for $m\in\mathbb R$ and $\mathbb V(x)= x^{1} ( \nu \mathbb{I}_4 +\mu \beta i \lambda ... 
Sparse bounds for maximal rough singular integrals via the Fourier transform
(Annales de l'institut Fourier, 20190312)We prove a quantified sparse bound for the maximal truncations of convolutiontype singular integrals with suitable Fourier decay of the kernel. Our result extends the sparse domination principle by CondeAlonso, Culiuc, ... 
The excluded volume of twodimensional convex bodies: shape reconstruction and nonuniqueness
(Journal of Physics A: Mathematical and Theoretical, 20190205)In the Onsager model of onecomponent hardparticle systems, the entire phase behaviour is dictated by a function of relative orientation, which represents the amount of space excluded to one particle by another at this ... 
Asymptotic models for free boundary flow in porous media
(Physica D, 2019)We provide rigorous asymptotic models for the free boundary Darcy and Forchheimer problem under the assumption of weak nonlinear interaction, in a regime in which the steepness parameter of the interface is considered to ... 
On the influence of gravity on densitydependent incompressible periodic fluids
(J. Differential Equations, 2019)The present work is devoted to the analysis of densitydependent, incompressible fluids in a 3D torus, when the Froude number $\varepsilon$ goes to zero. We consider the very general case where the initial data do not have ... 
Unique determination of the electric potential in the presence of a fixed magnetic potential in the plane
(201812)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 quasilinearities appearing in diffusion equations
(201812)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 ... 
Correlation imaging in inverse scattering is tomography on probability distributions
(Inverse Problems, 20181204)Scattering from a nonsmooth 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 ... 
Twoweight mixed norm estimates for a generalized spherical mean Radon transform acting on radial functions
(SIAM Journal on Mathematical Analysis, 2018)We investigate a generalized spherical means operator, viz. generalized spherical mean Radon transform, acting on radial functions. We establish an integral representation of this operator and find precise estimates of ... 
Vectorvalued extensions for fractional integrals of Laguerre expansions
(Studia Math., 2018)We prove some vectorvalued inequalities for fractional integrals defined for several orthonormal systems of Laguerre functions. On the one hand, we obtain weighted $L^pL^q$ vectorvalued extensions, in a multidimensional ... 
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 $L$ ... 
Nonlocal discrete diffusion equations and the fractional discrete Laplacian, regularity and applications
(Adv. Math., 2018)The analysis of nonlocal discrete equations driven by fractional powers of the discrete Laplacian on a mesh of size $h>0$ \[ (\Delta_h)^su=f, \] for $u,f:\Z_h\to\R$, $0<s<1$, is performed. The pointwise nonlocal ... 
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 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 ...