Now showing items 29-48 of 240

• #### The Calderón problem with corrupted data ﻿

(2017-01)
We consider the inverse Calderón problem consisting of determining the conductivity inside a medium by electrical measurements on its surface. Ideally, these measurements determine the Dirichlet-to-Neumann map and, therefore, ...
• #### Carleman type inequalities for fractional relativistic operators ﻿

(2019-09-22)
In this paper, we derive Carleman estimates for the fractional relativistic operator. Firstly, we consider changing-sign solutions to the heat equation for such operators. We prove monotonicity inequalities and convexity ...
• #### Cavity Volume and Free Energy in Many-Body Systems ﻿

(2021-10-01)
Within this work, we derive and analyse an expression for the free energy of a single-species system in the thermodynamic limit in terms of a generalised cavity volume, that is exact in general, and in principle applicable ...
• #### A characterization of two weight norm inequality for Littlewood-Paley $g_{\lambda}^{*}$-function ﻿

(2017)
Let $n\ge 2$ and $g_{\lambda}^{*}$ be the well-known high dimensional Littlewood-Paley function which was defined and studied by E. M. Stein, g_{\lambda}^{*}(f)(x)=\bigg(\iint_{\mathbb R^{n+1}_{+}} \Big(\frac{t}{t+|x-y ...
• #### A comparison principle for vector valued minimizers of semilinear elliptic energy, with application to dead cores ﻿

(2021)
We establish a comparison principle providing accurate upper bounds for the modulus of vector valued minimizers of an energy functional, associated when the potential is smooth, to elliptic gradient systems. Our assumptions ...
• #### Convergence over fractals for the Schrödinger equation ﻿

(2021-01)
We consider a fractal refinement of the Carleson problem for the Schrödinger equation, that is to identify the minimal regularity needed by the solutions to converge pointwise to their initial data almost everywhere with ...
• #### Convex Integration Arising in the Modelling of Shape-Memory Alloys: Some Remarks on Rigidity, Flexibility and Some Numerical Implementations ﻿

(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 ...
• #### Correlation imaging in inverse scattering is tomography on probability distributions ﻿

(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 ...
• #### Corrigendum to: An extension problem and trace Hardy inequality for the sublaplacian on H-type groups ﻿

(2021-03-10)
Recently we have found a couple of errors in our paper entitled An extension problem and trace Hardy inequality for the sub-Laplacian on $H$-type groups, Int. Math. Res. Not. IMRN (2020), no. 14, 4238--4294. They concern ...
• #### Counterexamples for the fractal Schrödinger convergence problem with an Intermediate Space Trick ﻿

(2021-12-09)
We construct counterexamples for the fractal Schrödinger convergence problem by combining a fractal extension of Bourgain's counterexample and the intermediate space trick of Du--Kim--Wang--Zhang. We confirm that the same ...
• #### Cubic microlattices embedded in nematic liquid crystals: A Landau-de Gennes study ﻿

(2021-01-01)
We consider a Landau-de Gennes model for a connected cubic lattice scaffold in a nematic host, in a dilute regime. We analyse the homogenised limit for both cases in which the lattice of embedded particles presents or not ...
• #### A Decomposition of Calderón–Zygmund Type and Some Observations on Differentiation of Integrals on the Infinite-Dimensional Torus ﻿

(2020-02-13)
In this note we will show a Calder\'on--Zygmund decomposition associated with a function $f\in L^1(\mathbb{T}^{\omega})$. The idea relies on an adaptation of a more general result by J. L. Rubio de Francia in the setting ...
• #### Defects in Nematic Shells: a Gamma-convergence discrete-to-continuum approach ﻿

(2018-07)
In this paper we rigorously investigate the emergence of defects on Nematic Shells with a genus different from one. This phenomenon is related to a non-trivial interplay between the topology of the shell and the alignment ...
• #### Degenerate Poincare-Sobolev inequalities ﻿

(2021)
Abstract. We study weighted Poincar ́e and Poincar ́e-Sobolev type in- equalities with an explicit analysis on the dependence on the Ap con- stants of the involved weights. We obtain inequalities of the form with different ...
• #### Derivation of limit equation for a singular perturbation of a 3D periodic Boussinesq system ﻿

(2017-07-15)
We consider a system describing the dynamics of an hydrodynamical, density-dependent flow under the effects of gravitational forces. We prove that if the Froude number is sufficiently small such system is globally well ...
• #### Design of effective bulk potentials for nematic liquid crystals via colloidal homogenisation ﻿

(2020-02-01)
We consider a Landau–de Gennes model for a suspension of small colloidal inclusions in a nematic host. We impose suitable anchoring conditions at the boundary of the inclusions, and we work in the dilute regime — i.e. the ...
• #### Determination of convection terms and quasi-linearities appearing in diffusion equations ﻿

(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 ...
• #### Dimension reduction for the micromagnetic energy functional on curved thin films ﻿

(2016-12-14)
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 ...
• #### Dirac Operators and Shell Interactions: A Survey ﻿

(2021-01-01)
In this survey we gather recent results on Dirac operators coupled with δ-shell interactions. We start by discussing recent advances regarding the question of self-adjointness for these operators. Afterwards we switch to ...