Related papers: Green's Functions for Stieltjes Boundary Problems
A new perspective of the Green's function in a boundary value problem as the only eigenstate in an auxiliary formulation is introduced. In this treatment, the Green's function can be perceived as a defect state in the presence of a…
We derive a closed-form expression for the Green function of linear evolution equations with the Dirichlet boundary condition for an arbitrary region, based on the singular perturbation approach to boundary problems.
Optimal pointwise estimates are derived for the biharmonic Green function under Dirichlet boundary conditions in arbitrary $C^{4,\gamma}$-smooth domains. Maximum principles do not exist for fourth order elliptic equations and the Green…
Green's function plays a significant role in both theoretical analysis and numerical computing of partial differential equations (PDEs). However, in most cases, Green's function is difficult to compute. The troubles arise in the following…
The aim of this study is to investigate a class of generalized boundary value transmission problems (BVTP's) for Sturm-Liouville equation on two separate intervals. We introduce modified inner product in direct sum space $L_{2}[a,c)\oplus…
In this paper, new representations of the Green's function for an acoustic d-dimensional half-space problem with impedance boundary conditions are presented. The main features of the new representation are: a) in addition to additive terms…
In this paper, we investigate the existence of positive solutions for a nonlocal fractional boundary value problem involving Caputo fractional derivative and nonlocal Riemann-Stieltjes integral boundary condition. By using the spectral…
We study global properties of Dirichlet forms such as uniqueness of the Dirichlet extension, stochastic completeness and recurrence. We characterize these properties by means of vanishing of a boundary term in Green's formula for functions…
We study questions related to critical points of the Green's function of a bounded multiply connected domain in the complex plane. The motion of critical points, their limiting positions as the pole approaches the boundary and the…
This paper investigates the Dirichlet problem for a non-divergence form elliptic operator $L$ in a bounded domain of $\mathbb{R}^d$. Under certain conditions on the coefficients of $L$, we first establish the existence of a unique Green's…
In this work, the first initial-boundary value problem for a sub-diffusion equation involving the regularized Prabhakar fractional derivative is studied. The problem is solved by reducing it to two initial-boundary value problems using the…
We establish the existence, uniqueness, and various estimates for Green functions of mixed Dirichlet-conormal derivative problems for the stationary Stokes system with measurable coefficients in a two-dimensional Reifenberg flat domain with…
Recently, an exact Green's function of the diffusion equation for a pair of spherical interacting particles in two dimensions subject to a backreaction boundary condition was used to derive an exact expression for the average lifetime of…
We construct Green's functions for divergence form, second order parabolic systems in non-smooth time-varying domains whose boundaries are locally represented as graph of functions that are Lipschitz continuous in the spatial variables and…
A class of scalar Stieltjes like functions is realized as linear-fractional transformations of transfer functions of conservative systems based on a Schr\"odinger operator T_h in $L_2[a,+\infty)$ with a non-selfadjoint boundary condition.…
Singular Green operators G appear typically as boundary correction terms in resolvents for elliptic boundary value problems on a domain \Omega \subset R^n, and more generally they appear in the calculus of pseudodifferential boundary…
We construct the fundamental solution or Green function for a divergence form elliptic system in two dimensions with bounded and measurable coefficients. We consider the elliptic system in a Lipschitz domain with mixed boundary conditions.…
We study estimates of the Green's function in $\mathbb{R}^d$ with $d \ge 2$, for the linear second order elliptic equation in divergence form with variable uniformly elliptic coefficients. In the case $d \ge 3$, we obtain estimates on the…
We prove the existence and pointwise bounds of the Green functions for stationary Stokes systems with measurable coefficients in two dimensional domains. We also establish pointwise bounds of the derivatives of the Green functions under a…
We investigate a first boundary value problem for a second-order partial differential equation involving the Prabhakar fractional derivative in time. Using structural properties of the Prabhakar kernel and generalized Mittag-Leffler…