An Elementary Proof That the Biharmonic Green Function of an Eccentric Ellipse Changes Sign

SIAM Review ◽  
1994 ◽  
Vol 36 (1) ◽  
pp. 99-101 ◽  
Author(s):  
Harold S. Shapiro ◽  
Max Tegmark
Keyword(s):  
Green Function ◽  
Elementary Proof ◽  
Biharmonic Green Function

scholarly journals Biharmonic Green function of a ring domain

2010 ◽  
Vol 106 (2) ◽  
pp. 267 ◽  
Author(s):  
Tatyana S. Vaitekhovich
Keyword(s):  
Green Function ◽  
Circular Ring ◽  
Ring Domain ◽  
Biharmonic Function ◽  
Biharmonic Green Function

A biharmonic Green function of a circular ring domain $R=\{z\in \mathsf {C}: 0<r<|z|<1\}$ is found in the form 26741 \widehat{G}_{2}(z,\zeta)=|\zeta-z|^{2}G_{1}(z,\zeta)+\widehat{h}_{2}(z,\zeta), 26741 where $G_{1}(z,\zeta)$ is the harmonic Green function of the ring $R$, and $\widehat{h}_{2}(z,\zeta)$ is a specially constructed biharmonic function.

AN ELEMENTARY PROOF OF A THEOREM OF LEE

1991 ◽  
Vol 11 (3) ◽  
pp. 356-360 ◽  
Author(s):  
Jia'an Yan
Keyword(s):  
Elementary Proof

Exponentially Convergent Approximation to the Elliptic Solution Operator

2006 ◽  
Vol 6 (4) ◽  
pp. 386-404 ◽  
Author(s):  
Ivan. P. Gavrilyuk ◽  
V.L. Makarov ◽  
V.B. Vasylyk
Keyword(s):  
Green Function ◽  
Boundary Value Problem ◽  
Elliptic Boundary ◽  
Boundary Value ◽  
Solution Operator ◽  
Hyperbolic Operator ◽  
Elliptic Solution ◽  
Elliptic Boundary Value ◽  
Sine Family ◽  
The Green Function

AbstractWe develop an accurate approximation of the normalized hyperbolic operator sine family generated by a strongly positive operator A in a Banach space X which represents the solution operator for the elliptic boundary value problem. The solution of the corresponding inhomogeneous boundary value problem is found through the solution operator and the Green function. Starting with the Dunford — Cauchy representation for the normalized hyperbolic operator sine family and for the Green function, we then discretize the integrals involved by the exponentially convergent Sinc quadratures involving a short sum of resolvents of A. Our algorithm inherits a two-level parallelism with respect to both the computation of resolvents and the treatment of different values of the spatial variable x ∈ [0, 1].

scholarly journals A new elementary proof of a theorem of Minkowski

1926 ◽  
Vol 2 (3) ◽  
pp. 97-99
Author(s):  
Matsusaburô Fujiwara
Keyword(s):  
Elementary Proof
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