• Monotonicity and convexity of the ratios of the first kind modified Bessel functions and applications 

  Yang Z-H.; Zheng S. (Mathematical Inequalities & Applications, 2017-07-18)

  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) ...

• Hartree-Fock theory with a self-generated magnetic field 

  Comelli S.; Garcia-Cervera C.J. (Journal of Mathematical Physics, 2017-06-01)

  We prove the existence of a ground state within the Hartree-Fock theory for atoms and molecules, in the presence of self-generated magnetic fields, with and without direct spin coupling. The ground state exists provided ...

• Sharp bounds for the ratio of modified Bessel functions 

  Zheng S.; Yang Z-H. (Mediterranean Journal of Mathematics, 2017-06-21)

  Let $I_{\nu }\left( x\right) $ be the modified Bessel functions of the first kind of order $\nu $, and $S_{p,\nu }\left( x\right) =W_{\nu }\left( x\right) ^{2}-2pW_{\nu }\left( x\right) -x^{2}$ with $W_{\nu }\left( x\right) ...

• Lorentz estimates for asymptotically regular fully nonlinear parabolic equations 

  Zhang J.; Zheng S. (Mathematische Nachrichten, 2017-06-20)

  We prove a global Lorentz estimate of the Hessian of strong solutions to the Cauchy-Dirichlet problem for a class of fully nonlinear parabolic equations with asymptotically regular nonlinearity over a bounded $C^{1,1}$ ...

• Some remarks on the $L^p$ regularity of second derivatives of solutions to non-divergence elliptic equations and the Dini condition 

  Escauriaza L.; Montaner S. (Rendiconti Lincei - Matematica e Applicazioni, 2017-05-30)

  In this note we prove an end-point regularity result on the $L^P$ integrability of the second derivatives of solutions to non-divergence form uniformly elliptic equations whose second derivatives are a priori only known ...

• Gaussian Decay of Harmonic Oscillators and related models 

  Cassano B.; Fanelli L. (Journal of Mathematical Analysis and Applications, 2017-05-15)

  We prove that the decay of the eigenfunctions of harmonic oscillators, uniform electric or magnetic fields is not stable under 0-order complex perturbations, even if bounded, of these Hamiltonians, in the sense that we can ...

• An efficient multigrid strategy for large-scale molecular mechanics optimization 

  Chen J.; García-Cervera C.J. (Journal of Computational Physics, 2017-08-01)

  Static mechanical properties of materials require large-scale nonlinear optimization of the molecular mechanics model under various controls. This paper presents an efficient multigrid strategy to solve such problems. This ...

• A quantitative approach to weighted Carleson condition 

  Rivera-Ríos I.P. (Concrete Operators, 2017-05-05)

  Quantitative versions of weighted estimates obtained by F. Ruiz and J.L. Torrea for the operator \[ \mathcal{M}f(x,t)=\sup_{x\in Q,\,l(Q)\geq t}\frac{1}{|Q|}\int_{Q}|f(x)|dx \qquad x\in\mathbb{R}^{n}, \, t \geq0 \] are ...

• Sparse domination theorem for multilinear singular integral operators with $L^{r}$-Hörmander condition 

  Li K. (Michigan Mathematical Journal, 2017-04-01)

  In this note, we show that if $T$ is a multilinear singular integral operator associated with a kernel satisfies the so-called multilinear $L^{r}$-Hörmander condition, then $T$ can be dominated by multilinear sparse operators.

• A characterization of two weight norm inequality for Littlewood-Paley $g_{\lambda}^{*}$-function 

  Cao M.; Li K.; Xue Q. (Journal of Geometric Analysis, 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 ...

• Quantitative weighted estimates for rough homogeneous singular integrals 

  Hytönen T. P.; Roncal L.; Tapiola O. (Israel Journal of Mathematics, 2017-03-11)

  We consider homogeneous singular kernels, whose angular part is bounded, but need not have any continuity. For the norm of the corresponding singular integral operators on the weighted space $L^2(w)$, we obtain a bound ...

• The Calderón problem with corrupted data 

  Caro P.; García A. (Inverse Problems, 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, ...

• Inverse scattering for a random potential 

  Caro P.; Helin T.; Lassas M. (2016-05)

  In this paper we consider an inverse problem for the $n$-dimensional random Schrödinger equation $(\Delta-q+k^2)u = 0$. We study the scattering of plane waves in the presence of a potential $q$ which is assumed to be a ...

• Global Uniqueness for The Calderón Problem with Lipschitz Conductivities 

  Caro P.; Rogers K.M. (Forum of Mathematics, Pi, 2016-01-01)

  We prove uniqueness for the Calderón problem with Lipschitz conductivities in higher dimensions. Combined with the recent work of Haberman, who treated the three- and four-dimensional cases, this confirms a conjecture of ...

• Uniqueness properties for discrete equations and Carleman estimates 

  Fernández Bertolin A.; Vega L. (Journal of Functional Analysis, 2017-03-25)

  Using Carleman estimates, we give a lower bound for solutions to the discrete Schrödinger equation in both dynamic and stationary settings that allows us to prove uniqueness results, under some assumptions on the decay of ...

• Singularity formation for the 1-D cubic NLS and the Schrödinger map on $\mathbb{S}^2$ 

  Banica V.; Vega L. (2017-02-02)

  In this note we consider the 1-D cubic Schrödinger equation with data given as small perturbations of a Dirac-$\delta$ function and some other related equations. We first recall that although the problem for this type of ...

• Partial regularity and smooth topology-preserving approximations of rough domains 

  Ball J.M.; Zarnescu A. (Calculus of Variations and Partial Differential Equations, 2017-01-01)

  For a bounded domain $\Omega\subset\mathbb{R}^m, m\geq 2,$ of class $C^0$, the properties are studied of fields of `good directions', that is the directions with respect to which $\partial\Omega$ can be locally represented ...

• Liquid crystal defects in the Landau–de Gennes theory in two dimensions — Beyond the one-constant approximation 

  Kitavtsev G.; Robbins J.M.; Slastikov V.; Zarnescu A. (Mathematical Models and Methods in Applied Sciences, 2016-12-31)

  We consider the two-dimensional Landau-de 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 ...

• Hardy uncertainty principle, convexity and parabolic evolutions 

  Escauriaza L.; Kenig C.; Ponce G.; Vega L. (Communications in Mathematical Physics, 2016-09-01)

  We give a new proof of the $L^2$ version of Hardy’s uncertainty principle based on calculus and on its dynamical version for the heat equation. The reasonings rely on new log-convexity properties and the derivation of ...

• A strategy for self-adjointness of Dirac operators: Applications to the MIT bag model and delta-shell interactions 

  Ourmières-Bonafos T.; Vega L. (2016-12-21)

  We develop an approach to prove self-adjointness of Dirac operators with boundary or transmission conditions at a $C^2$-compact surface without boundary. To do so we are lead to study the layer potential induced by the ...

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