Related papers: The Green function for the mixed problem for the l…
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…
We study the Green function for the stationary Stokes system with bounded measurable coefficients in a bounded Lipschitz domain $\Omega\subset \mathbb{R}^n$, $n\ge 3$. We construct the Green function in $\Omega$ under the condition…
We construct Green functions of conormal derivative problems for the stationary Stokes system with measurable coefficients in a two dimensional Reifenberg flat domain.
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 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.…
A mixed boundary value problem for the Stokes system in a polyhedral domain is considered. Here different boundary conditions (in particular, Dirichlet, Neumann, free surface conditions) are prescribed on the sides of the polyhedron. The…
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…
We study Green functions for stationary Stokes systems satisfying the conormal derivative boundary condition. We establish existence, uniqueness, and various estimates for the Green function under the assumption that weak solutions of the…
The paper deals with a mixed boundary value problem for the Stokes system in a polyhedral cone. Here different boundary conditions (in particular, Dirichlet, Neumann, free surface conditions) are prescribed on the sides of the polyhedron.…
We provide explicit formulas for the Green function of an elliptic PDE in the infinite strip and the half-plane. They are expressed in elementary and special functions. Proofs of uniqueness and existence are also given.
We study several quantities associated to the Green's function of a multiply connected domain in the complex plane. Among them are some intrinsic properties such as geodesics, curvature, and $L^2$-cohomology of the capacity metric and…
We study Green functions for the pressure of stationary Stokes systems in a (possibly unbounded) domain $\Omega\subset \mathbb{R}^d$, where $d\ge 2$. We construct the Green function when coefficients are merely measurable in one direction…
In this paper we analyse some possibilities of finding positive solutions for second order boundary value problems with Dirichlet and periodic boundary conditions, for which the correspondent Green's functions change sign. The obtained…
We construct an expression for the Green function of a differential operator satisfying nonlocal, homogeneous boundary conditions starting from the fundamental solution of the differential operator. This also provides the solution to the…
In this paper we will show several properties of the Green's functions related to various boundary value problems of arbitrary even order. In particular, we will write the expression of the Green's functions related to the general…
We give a novel vorticity formulation for the 3D Navier-Stokes equations with Dirichlet boundary conditions. Via a resolvent argument, we obtain Green's function and establish an upper bound, which is the 3D analog of [24]. Moreover, we…
In this article, the Green function for the Stokes flow in the interior, exterior, and annular regions bounded by cylindrical walls is derived as a function of the pole position and expressed invariantly both at the field and pole points.…
Necessary and sufficient conditions for Lipschitzness of the Lempert and Green functions are found in terms of their boundary behaviors.
We give some remarks on some manifolds K3 surfaces, Complex projective spaces, real projective space and Torus and the classification of two dimensional Riemannian surfaces, Green functions and the Stokes formula. We also, talk about traces…
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.