• Bloom type upper bounds in the product BMO setting 

  Li K.; Martikainen H.; Vuorinen E. (Journal of Geometric Analysis, 2019-04-08)

  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 Shape-Memory Alloys: Some Remarks on Rigidity, Flexibility and Some Numerical Implementations 

  Rüland, A.; Taylor J. M.; Zillinger, C. (Journal of Nonlinear Science, 2019-03-30)

  We study convex integration solutions in the context of the modelling of shape-memory alloys. The purpose of the article is twofold, treating both rigidity and flexibility prop- erties: Firstly, we relate the maximal ...

• Topological singular set of vector-valued maps, I: application to manifold-constrained Sobolev and BV spaces 

  Canevari G.; Orlandi G. (Calculus of Variations and Partial Differential Equations, 2019-03-30)

  We introduce an operator $\mathbf{S}$ on vector-valued 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 Landau-de Gennes study 

  Wang Y.; Canevari G.; Majumdar A. (SIAM Journal on Applied Mathematics, 2019-03-30)

  e study a modified Landau-de 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 three-dimensional ...

• Bloom type inequality for bi-parameter singular integrals: efficient proof and iterated commutators 

  Li K.; Martikainen H.; Vuorinen E. (International Mathematics Research Notices, 2019-03-14)

  Utilising some recent ideas from our bilinear bi-parameter theory, we give an efficient proof of a two-weight Bloom type inequality for iterated commutators of linear bi-parameter singular integrals. We prove that if $T$ ...

• Boundary Triples for the Dirac Operator with Coulomb-Type Spherically Symmetric Perturbations 

  Cassano B.; Pizzichillo F. (Journal of Mathematical Physics, 2019-02)

  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 

  Di Plinio F.; Hytönen T.; Li K. (Annales de l'institut Fourier, 2019-03-12)

  We prove a quantified sparse bound for the maximal truncations of convolution-type singular integrals with suitable Fourier decay of the kernel. Our result extends the sparse domination principle by Conde-Alonso, Culiuc, ...

• The excluded volume of two-dimensional convex bodies: shape reconstruction and non-uniqueness 

  Taylor J. M. (Journal of Physics A: Mathematical and Theoretical, 2019-02-05)

  In the Onsager model of one-component hard-particle 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 

  Granero-Belinchón R.; Scrobogna S. (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 density-dependent incompressible periodic fluids 

  Ngo V.-S.; Scrobogna S. (J. Differential Equations, 2019)

  The present work is devoted to the analysis of density-dependent, 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 

  Caro P.; Rogers K. (2018-12)

  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 quasi-linearities appearing in diffusion equations 

  Caro P.; Kian Y. (2018-12)

  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 

  Caro P.; Helin T.; Kujanpää A.; Lassas M. (Inverse Problems, 2018-12-04)

  Scattering from a non-smooth 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 ...

• Two-weight mixed norm estimates for a generalized spherical mean Radon transform acting on radial functions 

  Ciaurri Ó.; Nowak, A.; Roncal, L. (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 ...

• Vector-valued extensions for fractional integrals of Laguerre expansions 

  Ciaurri Ó.; Roncal L. (Studia Math., 2018)

  We prove some vector-valued inequalities for fractional integrals defined for several orthonormal systems of Laguerre functions. On the one hand, we obtain weighted $L^p-L^q$ vector-valued extensions, in a multidimensional ...

• Hölder-Lebesgue regularity and almost periodicity for semidiscrete equations with a fractional Laplacian 

  Lizama C.; Roncal L. (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 

  Ciaurri Ó.; Roncal L.; Stinga P.R.; Torrea J.L.; Varona J.L. (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 ...

• Hardy-type inequalities for fractional powers of the Dunkl-Hermite operator 

  Ciaurri Ó.; Roncal L.; Thangavelu S. (Proc. Edinburgh Math. Soc. (2), 2018)

  We prove Hardy-type inequalities for a fractional Dunkl–Hermite operator, which incidentally gives Hardy inequalities for the fractional harmonic oscillator as well. The idea is to use h-harmonic expansions to reduce the ...

• A Global well-posedness result for the Rosensweig system of ferrofluids 

  Scrobogna S.; De Anna F. (Rev. Mat. Iberoam., 2019)

  In this Paper we study a Bloch-Torrey regularization of the Rosensweig system for ferrofluids. The scope of this paper is twofold. First of all, we investigate the existence and uniqueness of Leray-Hopf solutions of this ...

• Vector-valued operators, optimal weighted estimates and the $C_p$ condition 

  Cejas M.E.; Li K.; Pérez C.; Rivera-Ríos I.P. (Science China Mathematics, 2018-09)

  In this paper some new results concerning the $C_p$ classes introduced by Muckenhoupt and later extended by Sawyer, are provided. In particular we extend the result to the full range expected $p>0$, to the weak norm, to ...

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