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Equations arising in General Relativity are usually too complicated to be solved analytically and one has to rely on numerical methods to solve sets of coupled partial differential equations. Among the possible choices, this paper focuses…
The general, multidimensional barrier crossing problem for diffusive processes under the action of conservative forces is studied with the goal of developing tractable approximations. Particular attention is given to the effect of different…
We study the spectrum of a periodic non-self-adjoint Dirac operator, and its dependence on a semiclassical parameter is also considered. Several bounds on the spectrum are obtained which provide sharp spectral enclosure estimates.…
The monitoring and management of high-volume feature-rich traffic in large networks offers significant challenges in storage, transmission and computational costs. The predominant approach to reducing these costs is based on performing a…
We establish the existence of weak solutions of a nonlinear radiation-type boundary value problem for elliptic equation on divergence form with discontinuous leading coefficient. Quantitative estimates play a crucial role on the real…
We study the solvability of boundary-value problems for differential-operator equations of the second order in L p (0, 1; X), with 1 < p < +$\infty$, X being a UMD complex Banach space. The originality of this work lies in the fact that we…
A spectral decomposition method is used to obtain solutions to a class of nonlinear differential equations. We extend this approach to the analysis of the fractional form of these equations and demonstrate the method by applying it to the…
We present a new solver for coupled nonlinear elliptic partial differential equations (PDEs). The solver is based on pseudo-spectral collocation with domain decomposition and can handle one- to three-dimensional problems. It has three…
We prove a limiting absorption principle for a generalized Helmholtz equation on an exterior domain with Dirichlet boundary conditions \begin{equation*} (L+\lambda)v=f, \qquad \lambda\in \mathbb{R} \end{equation*} under a Sommerfeld…
The present paper is devoted to study the asymptotic behavior of a sequence of linear elliptic equations with a varying drift term, whose coefficients are just bounded in $L^N(\Omega)$, with $N$ the dimension of the space. It is known that…
We develop a linear-algebraic framework for dimensional analysis in systems with constraints, particularly when variables are numerous or related by implicit relations so that direct elimination is impractical. By expressing both…
We make a distinction between the spectroscopic and the mesoscopic conductance of closed systems. We show that the latter is not simply related to the Landauer conductance of the corresponding open system. A new ingredient in the theory is…
Recently, an approach for metallic superlattices based on the finite periodic systems theory was introduced \cite{Pereyra2020}. Unlike most, if not all, of the published approaches that are valid in the $n \rightarrow \infty $ limit, the…
We examine the discrete Laplacian acting on a triangular lattice, introducing long-range perturbations to both the metric and the potential. Our goal is to establish a Limiting Absorption Principle away from possible embedded eigenvalues.…
In this paper we present a differential approach to photo-polarimetric shape estimation. We propose several alternative differential constraints based on polarisation and photometric shading information and show how to express them in a…
Atomic norm minimization is a convex optimization framework to recover point sources from a subset of their low-pass observations, or equivalently the underlying frequencies of a spectrally-sparse signal. When the amplitudes of the sources…
An equation containing a fractional power of an elliptic operator of second order is studied for Dirichlet boundary conditions. Finite difference approximations in space are employed. The proposed numerical algorithm is based on solving an…
The limiting absorption principle in two-dimensional space is justified for a second-order elliptic operators. Necessary and sufficient conditions for the right-hand side are given for this principle to be valid.
We establish a limiting absorption principle for some long range perturbations of the Dirac systems at threshold energies. We cover multi-center interactions with small coupling constants. The analysis is reduced to study a family of…
We present an innovative approach to dimensional analysis, referred to as augmented dimensional analysis and based on a representation theorem for complete quantity functions with a scaling-covariant scalar representation. This new theorem,…