A Modified Integral Equation Method for the Electric Boundary-Value Problem for the Vector Helmholtz Equation

1980 ◽  
pp. 157-170
Author(s):  
Werner Knauff ◽  
Rainer Kress
Keyword(s):  
Integral Equation ◽  
Boundary Value Problem ◽  
Helmholtz Equation ◽  
Boundary Value ◽  
Integral Equation Method ◽  
Equation Method

The treatment of a Neumann boundary value problem for force-free fields by an integral equation method

1978 ◽  
Vol 82 (1-2) ◽  
pp. 71-86 ◽  
Author(s):  
Rainer Kress
Keyword(s):  
Integral Equation ◽  
Boundary Value Problem ◽  
Vector Fields ◽  
Integral Formula ◽  
Boundary Value ◽  
Neumann Boundary ◽  
Integral Equation Method ◽  
Equation Method ◽  
Fredholm Alternative ◽  
Neumann Boundary Value Problem

SynopsisA Neumann boundary value problem for the equation rot μ − λμ = u is considered. The approach is by an integral equation method based on Cauchy's integral formula for generalized harmonic vector fields. Results on existence and uniqueness are obtained in terms of the familiar Fredholm alternative.

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