Browsing Analysis of Partial Differential Equations (APDE) by Title
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Klein's Paradox and the Relativistic $\delta$shell Interaction in $\mathbb{R}^3$
(201711)Under certain hypothesis of smallness of the regular potential $\mathbf{V}$, we prove that the Dirac operator in $\mathbb{R}^3$ coupled with a suitable rescaling of $\mathbf{V}$, converges in the strong resolvent sense ... 
Landaude Gennes Corrections to the OseenFrank Theory of Nematic Liquid Crystals
(20200103)We study the asymptotic behavior of the minimisers of the Landaude Gennes model for nematic liquid crystals in a twodimensional domain in the regime of small elastic constant. At leading order in the elasticity constant, ... 
Liquid crystal defects in the Landau–de Gennes theory in two dimensions — Beyond the oneconstant approximation
(20161231)We consider the twodimensional Landaude Gennes energy with several elastic constants, subject to general $k$radially symmetric boundary conditions. We show that for generic elastic constants the critical points consistent ... 
Lorentz estimates for asymptotically regular fully nonlinear parabolic equations
(20170620)We prove a global Lorentz estimate of the Hessian of strong solutions to the CauchyDirichlet problem for a class of fully nonlinear parabolic equations with asymptotically regular nonlinearity over a bounded $C^{1,1}$ ... 
Lorentz estimates for the gradient of weak solutions to elliptic obstacle problems with partially BMO coefficients
(2017)We prove global Lorentz estimates for variable power of the gradient of weak solution to linear elliptic obstacle problems with small partially BMO coefficients over a bounded nonsmooth domain. Here, we assume that the ... 
Magnetic domaintwin boundary interactions in NiMnGa
(202004)The stress required for the propagation of twin boundaries in a sample with fine twins increases monotonically with ongoing deformation. In contrast, for samples with a single twin boundary, the stress exhibits a plateau ... 
Maximal estimates for a generalized spherical mean Radon transform acting on radial functions
(2020)We study a generalized spherical means operator, viz.\ generalized spherical mean Radon transform, acting on radial functions. As the main results, we find conditions for the associated maximal operator and its local ... 
Meanfield dynamics of the spinmagnetization coupling in ferromagnetic materials: Application to currentdriven domain wall motions
(20151231)In this paper, we present a meanfield model of the spinmagnetization coupling in ferromagnetic materials. The model includes nonisotropic diffusion for spin dynamics, which is crucial in capturing strong spinmagnetization ... 
Minimizers of a Landaude Gennes energy with a subquadratic elastic energy
(2019)We study a modified Landaude 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 threedimensional ... 
Mixed norm estimates for the Cesàro means associated with DunklHermite expansions
(2017)Our main goal in this article is to study mixed norm estimates for the Cesàro means associated with DunklHermite expansions on $\mathbb{R}^d$. These expansions arise when one considers the DunklHermite operator ... 
Mixed weak type estimates: Examples and counterexamples related to a problem of E. Sawyer
(20160101)In this paper we study mixed weighted weaktype inequal ities for families of functions, which can be applied to study classic operators in harmonic analysis. Our main theorem extends the key result from [CMP2]. 
Modeling cardiac structural heterogeneity via spacefractional differential equations
(2017)We discuss here the use of nonlocal models in space and fractional order operators in the characterisation of structural complexity and the modeling of propagation in heterogeneous biological tissues. In the specific, we ... 
Models for damped water waves
(2019)In this paper we derive some new weakly nonlinear asymptotic models describing viscous waves in deep water with or without surface tension effects. These asymptotic models take into account several different dissipative ... 
Monotonicity and convexity of the ratios of the first kind modified Bessel functions and applications
(20170718)Let $I_{v}\left( x\right) $ be modified Bessel functions of the first kind. We prove the monotonicity property of the function $x\mapsto I_{u}\left( x\right) I_{v}\left( x\right) /I_{\left( u+v\right) /2}\left( x\right) ... 
Multilinear operatorvalued calderónzygmund theory
(2020)We develop a general theory of multilinear singular integrals with operator valued kernels, acting on tuples of UMD Banach spaces. This, in particular, involves investigating multilinear variants of the Rboundedness ... 
Multilinear singular integrals on noncommutative lp spaces
(2019)We prove Lp bounds for the extensions of standard multilinear Calderón Zygmund operators to tuples of UMD spaces tied by a natural product structure. The product can, for instance, mean the pointwise product in UMD ... 
New bounds for bilinear CalderónZygmund operators and applications
(20161125)In this work we extend Lacey’s domination theorem to prove the pointwise control of bilinear Calderón–Zygmund operators with Dini–continuous kernel by sparse operators. The precise bounds are carefully tracked following ... 
Nonlocal discrete diffusion equations and the fractional discrete Laplacian, regularity and applications
(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 ... 
A note on generalized Poincarétype inequalities with applications to weighted improved Poincarétype inequalities
(2020)The main result of this paper supports a conjecture by C. P\'erez and E. Rela about the properties of the weight appearing in their recent selfimproving result of generalized inequalities of Poincar\'etype in the Euclidean ... 
A note on the offdiagonal MuckenhouptWheeden conjecture
(20160701)We obtain the offdiagonal MuckenhouptWheeden conjecture for CalderónZygmund operators. Namely, given $1 < p < q < \infty$ and a pair of weights $(u; v)$, if the HardyLittlewood maximal function satisfies the following ...