green functions

Derivatives of a volume integral with singular kernel

Hi everybody, 

In fact, I encounter this problem in my research and I would be grateful if someone can help. In micro mechanics, there are many problems concerning Green functions, e.g: the displacement is calculated from the distributed force in the domain, etc. Consider the following integral to determine the displacement field.

u(x)=∫A(x,y)dVy where A(x,y) is singular of order r-2 (i.e r2=(x-y)(x-y)).


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