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The aim of this paper is twofold. First, we prove $L^p$ estimates for a regularized Green's function in three dimensions. We then establish new estimates for the discrete Green's function and obtain some positivity results. In particular,…

Numerical Analysis · Mathematics 2023-12-29 Andrew Miller

Developing a reliable kinetic energy density functional within orbital-free density functional theory remains a long-standing challenge, particularly for atomic and molecular systems. A major difficulty lies in the absence of a systematic…

Chemical Physics · Physics 2025-10-22 Priya Priya , Anuvab Panda , Saswata Basu , Mainak Sadhukhan

In this paper we obtain the explicit expression of the Green's function related to a general $n$ order differential equation coupled to non-local linear boundary conditions. In such boundary conditions, a $n$ dimensional parameter…

Classical Analysis and ODEs · Mathematics 2021-07-13 Alberto Cabada , Lucía López-Somoza , Mouhcine Yousfi

We consider the large-scale regularity of solutions to second-order linear elliptic equations with random coefficient fields. In contrast to previous works on regularity theory for random elliptic operators, our interest is in the…

Analysis of PDEs · Mathematics 2016-10-26 Julian Fischer , Claudia Raithel

This paper is a revised version of the original paper of same title--published in Applied Mathematics Letters 89--containing some corrections and clarifications to the original text. We derive non-singular Green's functions for the…

Analysis of PDEs · Mathematics 2020-07-10 Mads Mølholm Hejlesen , Grégoire Winckelmans , Jens Honoré Walther

The two-dimensional elastodynamic Green tensor is the primary building block of solutions of linear elasticity problems dealing with nonuniformly moving rectilinear line sources, such as dislocations. Elastodynamic solutions for these…

Classical Physics · Physics 2015-06-09 Yves-Patrick Pellegrini , Markus Lazar

We obtain the Green's function $G$ for any flat rhombic torus $T$, always with numerical values of significant digits up to the fourth decimal place (noting that $G$ is unique for $|T|=1$ and $\int_TGdA=0$). This precision is guaranteed by…

Numerical Analysis · Mathematics 2025-09-17 A. E. D. Castillo , G. A. Lobos , V. Ramos Batista

We continue the development, by reduction to a first order system for the conormal gradient, of $L^2$ \textit{a priori} estimates and solvability for boundary value problems of Dirichlet, regularity, Neumann type for divergence form second…

Classical Analysis and ODEs · Mathematics 2015-05-20 Pascal Auscher , Andreas Rosén

We explore the connections between Green's functions for certain differential equations, covariance functions for Gaussian processes, and the smoothing splines problem. Conventionally, the smoothing spline problem is considered in a setting…

Statistics Theory · Mathematics 2021-02-08 Lars Lau Raket

We present a method for analytic continuation of retarded Green functions, including Euclidean Green functions computed using lattice QCD. The method is based on conformal maps and construction of an interpolation function which is analytic…

High Energy Physics - Lattice · Physics 2023-06-14 Thomas Bergamaschi , William I. Jay , Patrick R. Oare

We construct a series of charged dilatonic black holes which share zero entropy in the zero temperature limit using Einstein-Maxwell-Dilaton theories. In these black holes, the wave functions and the Green's functions of massless fermions…

High Energy Physics - Theory · Physics 2014-12-16 Zhong-Ying Fan

A formula relating quotients of determinants of elliptic differential operators sharing their principal symbol, with local boundary conditions, to the corresponding Green function is given.

The many-body Green's function provides access to electronic properties beyond density functional theory level in ab inito calculations. In this manuscript, we propose a deep learning framework for predicting the finite-temperature Green's…

Chemical Physics · Physics 2024-02-20 Xinyang Dong , Emanuel Gull , Lei Wang

We study a nonlinear system made up of an elliptic equation of blended singular/degenerate type and Poisson's equation with a lowly integrable source. We prove the existence of a weak solution in any space dimension and, chiefly, derive an…

Analysis of PDEs · Mathematics 2020-07-17 Edgard A. Pimentel , José Miguel Urbano

In this note we establish the positivity of Green's functions for a class of elliptic differential operators on closed, Riemannian manifolds.

Analysis of PDEs · Mathematics 2010-03-30 David T. Raske

We analyse the <VAP> three-point function of vector, axial-vector and pseudoscalar currents. In the spirit of large N_C, a resonance dominated Green function is confronted with the leading high-energy behaviour from the operator product…

High Energy Physics - Phenomenology · Physics 2009-11-10 V. Cirigliano , G. Ecker , M. Eidemuller , A. Pich , J. Portoles

The pointwise space-time behavior of the Green's function of the three-dimensional modified Vlasov-Poisson-Boltzmann system is studied in this paper. It is shown that the Green's function has a decomposition of the macroscopic diffusive…

Analysis of PDEs · Mathematics 2026-04-16 Yanchao Li , Luobin Qiu , Mingying Zhong

Under a largeness assumption on the size of the residue field, we give an explicit description of the positive-depth Deligne--Lusztig induction of unramified elliptic pairs $(T,\theta)$. When $\theta$ is regular, we show that positive-depth…

Representation Theory · Mathematics 2025-06-06 Charlotte Chan , Masao Oi

In this paper we prove a uniform estimate for the gradient of the Green function on a closed Riemann surface, independent of its conformal class, and we derive compactness results for immersions with L2-bounded second fundamental form and…

Differential Geometry · Mathematics 2013-07-23 Paul Laurain , Tristan Rivière

Flexible boundary condition methods couple an isolated defect to bulk through the bulk lattice Green's function. The inversion of the force-constant matrix for the lattice Green's function requires Fourier techniques to project out the…

Materials Science · Physics 2010-05-28 M. Ghazisaeidi , D. R. Trinkle