Related papers: On Multiple Frequency Power Density Measurements

In this paper we construct a parametrix for the fractional Helmholtz equation $((-\Delta)^s - \tau^{2s} r(x)^{2s} + q(x))u=0$ making use of geometrical optics solutions. We show that the associated eikonal equation is the same as in the…

We study the following version of Hardy-type inequality on a domain $\Omega$ in a Riemannian manifold $(M,g)$: $$ \int{\Omega}|\nabla u|_g^p\rho^\alpha dV_g \geq \left(\frac{|p-1+\beta|}{p}\right)^p\int{\Omega}\frac{|u|^p|\nabla…

In order to reconstruct the initial conditions of the universe it is important to devise a method that can efficiently constrain the shape of the power spectrum of primordial matter density fluctuations in a model-independent way from data.…

For $\Omega\subset \mathbb{R}^2$ a smooth and bounded domain, we derive a sharp universal energy estimate for non-negative solutions of free boundary problems on $\Omega$ arising in plasma physics. As a consequence, we are able to deduce…

Due to their intuitiveness, flexibility and relative numerical efficiency, the macroscopic Maxwell-Bloch (MB) equations are a widely used semiclassical and semi-phenomenological model to describe optical propagation and coherent…

We present a method to compute the photoionization spectra of atoms and molecules in linear response time-dependent density functional theory. The electronic orbital variations corresponding to ionized electrons are expanded on a basis set…

This paper concerns the reconstruction of a scalar diffusion coefficient $\sigma(x)$ from redundant functionals of the form $H_i(x)=\sigma^{2\alpha}(x)|\nabla u_i|^2(x)$ where $\alpha\in\Rm$ and $u_i$ is a solution of the elliptic problem…

Motivated by problems in control theory concerning decay rates for the damped wave equation $$w_{tt}(x,t) + \gamma(x) w_t(x,t) + (-\Delta + 1)^{s/2} w(x,t) = 0,$$ we consider an analogue of the classical Paneah-Logvinenko-Sereda theorem for…

Consider the following $m-$polyharmonic Kirchhoff problem: \begin{eqnarray} \label{ea} \begin{cases} M\left(\int_{\O}|D_r u|^{m} +a|u|^m\right)[\Delta^r_m u +a|u|^{m-2}u]= K(x)f(u) &\mbox{in}\quad \Omega, \\ u=\left(\frac{\partial}{\partial…

A basic concept to calculate physical features of non-ideal plasmas, such as optical properties, is the spectral function which is linked to the self-energy. We calculate the spectral function for a non-relativistic hydrogen plasma in…

A crucial role in the theory of uncertainty quantification (UQ) of PDEs is played by the regularity of the solution with respect to the stochastic parameters; indeed, a key property one seeks to establish is that the solution is holomorphic…

The orientation-preservation condition, i.e., the Jacobian determinant of the deformation gradient $\det \nabla u$ is required to be positive, is a natural physical constraint in elasticity as well as in many other fields. It is well known…

The primordial non-Gaussianity induces scale-dependent bias of the \hi with respect to the underlying dark matter, which exhibits features on the very large scales of the 21-cm power spectrum potentially observable with \hi intensity…

Hybrid inverse problems are mathematical descriptions of coupled-physics (also called multi-waves) imaging modalities that aim to combine high resolution with high contrast. The solution of a high-resolution inverse problem, a first step…

We study the Helmholtz equation with electromagnetic-type perturbations, in the exterior of a domain, in dimension $n\geq3$. We prove, by multiplier techniques in the sense of Morawetz, a family of a priori estimates from which the limiting…

We constrain two non-flat time-evolving dark energy cosmological models by using Hubble parameter data, Type Ia supernova apparent magnitude measurements, and baryonic acoustic oscillation peak length scale observations. The inclusion of…

We consider null geodesics in the background of spherically symmetric object in Einstein-Maxwell-Dilaton (EMD) theory with coupling function $f(\Phi)=e^{-2\lambda \Phi}$. The spherical solution is characteristically described by dilaton…

Huygens principle (HP) is the cornerstone of wave optics, its mathematical model is a boundary value problem of wave equation. The solutions of this mathematical model should be partial derivative u sub n independent and satisfy the form of…

We study the nonlinear diffusion equation $ u_t=\Delta\phi(u) $ on general Euclidean domains, with homogeneous Neumann boundary conditions. We assume that $ \phi^\prime(u) $ is bounded from below by $ |u|^{m_1-1} $ for small $ |u| $ and by…

We consider a bounded open subset $\Omega$ of ${\mathbb{R}}^n$ of class $C^{1,\alpha}$ for some $\alpha\in]0,1[$, and we define a distributional outward unit normal derivative for $\alpha$-H\"{o}lder continuous solutions of the Helmholtz…