• Quantitative weighted estimates for singular integrals and commutators 

  Rivera-Ríos I.P. (2018-02-27)

  In this dissertation several quantitative weighted estimates for singular integral op- erators, commutators and some vector valued extensions are obtained. In particular strong and weak type $(p, p)$ estimates, Coifman-Fe ...

• Variable Lorentz estimate for nonlinear elliptic equations with partially regular nonlinearities 

  Liang S.; Zheng S. (Nonlinear Analysis, 2018-02-15)

  We prove global Calder\'on-Zygmund type estimate in Lorentz spaces for variable power of the gradients to weak solution of nonlinear elliptic equations in a non-smooth domain. We mainly assume that the nonlinearities are ...

• Zero limit of entropic relaxation time for the Shliomis model of ferrofluids 

  Scrobogna S. (2018-02-11)

  We construct solutions for the Shilomis model of ferrofluids in a critical space, uniformly in the entropic relaxation time $ \tau \in (0, \tau_0) $. This allows us to study the convergence when $ \tau\to 0 $ for such solutions.

• Lorentz estimates for the gradient of weak solutions to elliptic obstacle problems with partially BMO coefficients 

  Zheng S.; Tian H. (Boundary Value Problems, 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 ...

• Weghted Lorentz and Lorentz-Morrey estimates to viscosity solutions of fully nonlinear elliptic equations 

  Junjie Zhang,Shenzhou Zheng (Complex Variables and Elliptic Equations, 2018)

  We prove a global weighted Lorentz and Lorentz-Morrey estimates of the viscosity solutions to the Dirichlet problem for fully nonlinear elliptic equation $F(D^{2}u,x)=f(x)$ defined in a bounded $C^{1,1}$ domain. The ...

• Bilinear representation theorem 

  Li K.; Martikainen H.; Ou Y.; Vuorinen E. (Transactions of the American Mathematical Society, 2018-01-01)

  We represent a general bilinear Calderón--Zygmund operator as a sum of simple dyadic operators. The appearing dyadic operators also admit a simple proof of a sparse bound. In particular, the representation implies a so ...

• Singular Perturbation of the Dirac Hamiltonian 

  Pizzichillo F. (2017-12-15)

  This thesis is devoted to the study of the Dirac Hamiltonian perturbed by delta-type potentials and Coulomb-type potentials. We analysed the delta-shell interaction on bounded and smooth domains and its approximation by ...

• Improved A1 − A∞ and related estimates for commutators of rough singular integrals 

  Rivera-Ríos I.P. (Proceedings of the Edinburgh Mathematical Society, 2017)

  An $A_1-A_\infty$ estimate improving a previous result in [22] for $[b, T_\Omega]$ with $\Omega\in L^\infty(S^{n-1})$ and $b\in BMO$ is obtained. Also a new result in terms of the $A_\infty$ constant and the one ...

• On a hyperbolic system arising in liquid crystal modelling 

  Fereisl E.; Rocca E.; Schimperna G.; Zarnescu A. (Journal of Hyperbolic Differential Equations, 2017-11)

  We consider a model of liquid crystals, based on a nonlinear hyperbolic system of differential equations, that represents an inviscid version of the model proposed by Qian and Sheng. A new concept of dissipative solution ...

• Sphere-valued harmonic maps with surface energy and the K13 problem 

  Day S.; Zarnescu A. (Advances in the Calculus of Variations, 2017-11)

  We consider an energy functional motivated by the celebrated K13 problem in the Oseen-Frank theory of nematic liquid crystals. It is defined for sphere-valued functions and appears as the usual Dirichlet energy with an ...

• Global well-posedness and twist-wave solutions for the inertial Qian-Sheng model of liquid crystals 

  de Anna F.; Zarnescu A. (Journal of Differential Equations, 2017-10-02)

  We consider the inertial Qian-Sheng model of liquid crystals which couples a hyperbolic-type equation involving a second-order material derivative with a forced incompressible Navier-Stokes system. We study the energy law ...

• Klein's Paradox and the Relativistic $\delta$-shell Interaction in $\mathbb{R}^3$ 

  Mas A; Pizzichillo F. (Analysis & PDE, 2017-11)

  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 re-scaling of $\mathbf{V}$, converges in the strong resolvent sense ...

• Asymptotic behaviour for fractional diffusion-convection equations 

  Ignat L.; Stan D. (2017-10)

  We consider a convection-diffusion model with linear fractional diffusion in the sub-critical range. We prove that the large time asymptotic behavior of the solution is given by the unique entropy solution of the convective ...

• Existence of weak solutions for a general porous medium equation with nonlocal pressure 

  Stan D.; del Teso F.; Vázquez JL. (submitted, 2017-10)

  We study the general nonlinear diffusion equation $u_t=\nabla\cdot (u^{m-1}\nabla (-\Delta)^{-s}u)$ that describes a flow through a porous medium which is driven by a nonlocal pressure. We consider constant parameters ...

• Three-dimensional coarsening dynamics of a conserved, nematic liquid crystal-isotropic fluid mixture 

  Nós R.L.; Roma A. M.; Garcia-Cervera C.J.; Ceniceros H.D. (Journal of Non-Newtonian Fluid Mechanics, 2017-09)

  We present a numerical investigation of the three-dimensional coarsening dynamics of a nematic liquid crystal-isotropic fluid mixture using a conserved phase field model. The model is a coupled system for a generalized ...

• Spectral asymptotics for $\delta$-interactions on sharp cones 

  Ourmières-Bonafos T.; Pankrashkin K.; Pizzichillo F. (Journal of Mathematical Analysis and Applications, 2017)

  We investigate the spectrum of three-dimensional Schr\"odinger operators with $\delta$-interactions of constant strength supported on circular cones. As shown in earlier works, such operators have infinitely many eigenvalues ...

• Weighted mixed weak-type inequalities for multilinear operators 

  Li K.; Ombrosi S.; Picardi B. (Studia Mathematica, 2017)

  In this paper we present a theorem that generalizes Sawyer's classic result about mixed weighted inequalities to the multilinear context. Let $\vec{w}=(w_1,...,w_m)$ and $\nu = w_1^\frac{1}{m}...w_m^\frac{1}{m}$, the main ...

• Mixed norm estimates for the Cesàro means associated with Dunkl-Hermite expansions 

  Boggarapu P.; Roncal L.; Thangavelu S. (Transactions of the American Mathematical Society, 2017)

  Our main goal in this article is to study mixed norm estimates for the Cesàro means associated with Dunkl--Hermite expansions on $\mathbb{R}^d$. These expansions arise when one considers the Dunkl--Hermite operator ...

• Dispersive effects of weakly compressible and fast rotating inviscid fluids 

  Ngo V.-S; Scrobogna S. (Discrete and Continuous Dynamical Systems - Series A, 2017-08)

  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 $. ...

• On pointwise and weighted estimates for commutators of Calderón-Zygmund operators 

  Lerner A. K; Ombrosi S.; Rivera-Ríos I.P. (Advances in Mathematics, 2017)

  In recent years, it has been well understood that a Calderón-Zygmund operator T is pointwise controlled by a finite number of dyadic operators of a very simple structure (called the sparse operators). We obtain a similar ...

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