### Recent Submissions

• #### 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, ...
• #### 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 ...
• #### 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 ...
• #### 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 $T$ ...
• #### Boundary Triples for the Dirac Operator with Coulomb-Type Spherically Symmetric Perturbations ﻿

(Journal of Mathematical Physics, 2019-02)