Browsing Analysis of Partial Differential Equations (APDE) by Title
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The Calderón problem with corrupted data
(201701)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 DirichlettoNeumann map and, therefore, ... 
Carleman type inequalities for fractional relativistic operators
(20190922)In this paper, we derive Carleman estimates for the fractional relativistic operator. Firstly, we consider changingsign solutions to the heat equation for such operators. We prove monotonicity inequalities and convexity ... 
A characterization of two weight norm inequality for LittlewoodPaley $g_{\lambda}^{*}$function
(2017)Let $n\ge 2$ and $g_{\lambda}^{*}$ be the wellknown high dimensional LittlewoodPaley function which was defined and studied by E. M. Stein, $$g_{\lambda}^{*}(f)(x)=\bigg(\iint_{\mathbb R^{n+1}_{+}} \Big(\frac{t}{t+xy ... 
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
(202101)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 ShapeMemory Alloys: Some Remarks on Rigidity, Flexibility and Some Numerical Implementations
(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 ... 
Correlation imaging in inverse scattering is tomography on probability distributions
(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 ... 
A Decomposition of Calderón–Zygmund Type and Some Observations on Differentiation of Integrals on the InfiniteDimensional Torus
(20200213)In this note we will show a Calder\'onZygmund 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 Gammaconvergence discretetocontinuum approach
(201807)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 nontrivial interplay between the topology of the shell and the alignment ... 
Degenerate PoincareSobolev inequalities
(2021)Abstract. We study weighted Poincar ́e and Poincar ́eSobolev 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
(20170715)We consider a system describing the dynamics of an hydrodynamical, densitydependent 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
(20200201)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 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 ... 
Dimension reduction for the micromagnetic energy functional on curved thin films
(20161214)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 ... 
Discreteness of transmission eigenvalues for higherorder main terms and perturbations
(20160701)In this paper we extend Sylvester's approach via upper triangular compact operators to establish the discreteness of transmission eigenvalues for higherorder main terms and higherorder perturbations. The coefficients of ... 
Discretizations of the spectral fractional Laplacian on general domains with Dirichlet, Neumann, and Robin boundary conditions
(20170428)In this work, we propose novel discretisations of the spectral fractional Laplacian on bounded domains based on the integral formulation of the operator via the heatsemigroup formalism. Specifically, we combine suitable ... 
Dispersive effects of weakly compressible and fast rotating inviscid fluids
(201708)We consider a system describing the motion of an isentropic, inviscid, weakly compressible, fast rotating fluid in the whole space $\mathbb{R}^3$, with initial data belonging to $ H^s \left( \mathbb{R}^3 \right), s>5/2 $. ... 
Double layered solutions to the extended Fisher–Kolmogorov P.D.E.
(20210622)We construct double layered solutions to the extended Fisher–Kolmogorov P.D.E., under the assumption that the set of minimal heteroclinics of the corresponding O.D.E. satisfies a separation condition. The aim of our work ... 
Dynamics and flow effects in the BerisEdwards system modeling nematic liquid crystals
(20180810)We consider the BerisEdwards system modelling incompressible liquid crystal flows of nematic type. This couples a NavierStokes system for the fluid velocity with a parabolic reactionconvectiondiffusion equation for the ... 
Echo Chains as a Linear Mechanism: Norm Inflation, Modified Exponents and Asymptotics
(20210730)In this article we show that the Euler equations, when linearized around a low frequency perturbation to Couette flow, exhibit norm inflation in Gevreytype spaces as time tends to infinity. Thus, echo chains are shown to ...