The elliptic boundary problem on the half space

1979 ◽  
Vol 4 (5) ◽  
pp. 537-554 ◽  
Author(s):  
Albert K. Erkip
Keyword(s):  
Boundary Problem ◽  
Half Space ◽  
Elliptic Boundary ◽  
Elliptic Boundary Problem

scholarly journals An elliptic boundary problem for a system involving a discontinuous weight

2002 ◽  
Vol 108 (3) ◽  
pp. 289-317 ◽  
Author(s):  
R Denk ◽  
M Faierman ◽  
M Möller
Keyword(s):  
Boundary Problem ◽  
Elliptic Boundary ◽  
Elliptic Boundary Problem

An elliptic boundary problem involving an indefinite weight

2000 ◽  
Vol 130 (2) ◽  
pp. 287-305 ◽  
Author(s):  
M. Faierman
Keyword(s):  
Weight Function ◽  
Boundary Problem ◽  
Spectral Theory ◽  
Positive Measure ◽  
Elliptic Boundary ◽  
Higher Order ◽  
Indefinite Weight ◽  
Boundary Problems ◽  
Elliptic Boundary Problem ◽  
Indefinite Weight Function

The spectral theory for non-self-adjoint elliptic boundary problems involving an indefinite weight function has only been established for the case of higher-order operators under the assumption that the reciprocal of the weight function is essentially bounded. In this paper we are concerned with the spectral theory for a case where the weight function vanishes on a set of positive measure.

scholarly journals Another approach to a non-elliptic boundary problem

1977 ◽  
Vol 66 ◽  
pp. 13-22 ◽  
Author(s):  
Yoshio Kato
Keyword(s):  
Boundary Value Problem ◽  
Boundary Problem ◽  
Bounded Domain ◽  
Elliptic Boundary ◽  
Boundary Value ◽  
Elliptic Boundary Value Problem ◽  
Elliptic Boundary Value ◽  
Elliptic Boundary Problem ◽  
Euclidian Space

Let Ω be a bounded domain in ndimensional Euclidian space Rn(n ≧ 2)with C∞boundary Γ of dimension n— 1 and let there be given two real-valued C∞–functions α, β on Γ such that α≧ 0, β ≧ 0and α + β = lthroughout Γ.Then we consider the non-elliptic boundary value problem with λ ≧ 0 (which is always assumed, and in particular when λ =0, we further assume β ≢ 0,throughout this paper) :(1)

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.

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