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Now showing items 11-20 of 20

#### Lorentz estimates for asymptotically regular fully nonlinear parabolic equations

(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 $C^{1,1}$ ...

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

(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 ...

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

(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

(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 ...

#### Discretizations of the spectral fractional Laplacian on general domains with Dirichlet, Neumann, and Robin boundary conditions

(2017-04-28)

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 heat-semigroup formalism. Specifically, we combine suitable ...

#### Uniqueness properties for discrete equations and Carleman estimates

(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 $\mathbb{S}^2$

(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 ...

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

(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 ...

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

(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 ...

#### Modeling cardiac structural heterogeneity via space-fractional differential equations

(Computational and Mathematical Biomedical Engineering (CMBE2017) Proceedings, 2017)

We discuss here the use of non-local 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 ...