Green's function of the general elliptic boundary problem with pseudodifferential boundary conditions

1972 ◽  
Vol 23 (6) ◽  
pp. 630-634 ◽  
Author(s):  
I. A. Kovalenko ◽  
Ya. A. Roitberg
Keyword(s):  
Boundary Conditions ◽  
Green’S Function ◽  
Boundary Problem ◽  
Green's Function ◽  
Elliptic Boundary ◽  
Elliptic Boundary Problem ◽  
General Elliptic ◽  
General Elliptic Boundary ◽  
Pseudodifferential Boundary

Eigenvalue asymptotics for an elliptic boundary problem

2007 ◽  
Vol 137 (2) ◽  
pp. 281-302 ◽  
Author(s):  
M. Faierman ◽  
M. Möller
Keyword(s):  
Boundary Conditions ◽  
Asymptotic Behaviour ◽  
Weight Function ◽  
Boundary Problem ◽  
Spectral Parameter ◽  
Elliptic Boundary ◽  
Bounded Region ◽  
Eigenvalue Asymptotics ◽  
Elliptic Boundary Problem ◽  
Parameter Condition

We consider an elliptic boundary problem in a bounded region Ω ⊂ ℝn wherein the spectral parameter is multiplied by a real-valued weight function with the property that it, together with its reciprocal, is essentially bounded in Ω. The problem is considered under limited smoothness assumptions and under an ellipticity with parameter condition. Then, fixing our attention upon the operator induced on L2(Ω) by the boundary problem under null boundary conditions, we establish results pertaining to the asymptotic behaviour of the eigenvalues of this operator under weaker smoothness assumptions than have hitherto been supposed.

An elliptic boundary problem involving a semi-definite weight

2004 ◽  
Vol 134 (1) ◽  
pp. 109-136 ◽  
Author(s):  
M. Faierman
Keyword(s):  
Boundary Conditions ◽  
Weight Function ◽  
Boundary Problem ◽  
Existence And Uniqueness ◽  
Spectral Properties ◽  
Elliptic Boundary ◽  
A Priori ◽  
Operator Pencil ◽  
Bounded Region ◽  
Elliptic Boundary Problem

We consider an elliptic boundary problem defined in a bounded region Ω ⊂ Rn and where the spectral parameter is multiplied by a weight function ω(x). We suppose that ω(x) ≠ 0 for x ∈ Ω, but vanishes in a specified manner on the boundary of Ω. Under limited smoothness assumptions, we derive results pertaining to existence and uniqueness of and a priori estimates for solutions of the boundary problem. If S(λ) denotes the operator pencil induced in L2(Ω) by the boundary problem with zero boundary conditions, then results are also derived pertaining to the spectral properties of S(λ).

A Liouville Type Theorem for Poly-harmonic System with Dirichlet Boundary Conditions in a Half Space

2015 ◽  
Vol 15 (1) ◽  
Author(s):  
Zhao Liu ◽  
Wei Dai
Keyword(s):  
Boundary Conditions ◽  
Green’S Function ◽  
Half Space ◽  
Green's Function ◽  
Dirichlet Boundary ◽  
Type Theorem ◽  
Dirichlet Boundary Conditions ◽  
Liouville Type ◽  
Liouville Type Theorem ◽  
Harmonic System

AbstractIn this paper, we consider the following poly-harmonic system with Dirichlet boundary conditions in a half space ℝwherewhereis the Green’s function in ℝ

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