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Now showing items 1-10 of 13

#### On extension problem, trace hardy and Hardy’s inequalities for some fractional Laplacians

(Communications on pure and applied analysis, 2019-09)

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, 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, ...

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

(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

(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 ...

#### Convex Integration Arising in the Modelling of Shape-Memory Alloys: Some Remarks on Rigidity, Flexibility and Some Numerical Implementations

(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 ...

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

(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 $T$ ...

#### Sparse bounds for maximal rough singular integrals via the Fourier transform

(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

(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 ...

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

(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 ...

#### Asymptotic behaviour of neuron population models structured by elapsed-time

(Nonlinearity, 2019-01-04)

We study two population models describing the dynamics of interacting neurons, initially proposed by Pakdaman et al (2010 Nonlinearity 23 55–75) and Pakdaman et al (2014 J. Math. Neurosci. 4 1–26). In the first model, the ...