The fourth boundary value problem

Suppose that in the volume V the potential obeys Poisson s equation  

If U and U2 are solutions of Poisson s equation and obey the boundary condition (1.94), their difference = U2—U1 satisfies Laplace s equation and the condition on the surface S  

Now consider again the equality (1.78) its left hand side can be either zero or positive, while, as follows from Equation (1.96), it is negative or zero. Therefore, Equation (1.78) takes place if both integrals are equal to zero and, correspondingly, 

In conclusion, let us summarize the main results derived in this section. 

Four types of boundary conditions have been formulated and each of them uniquely defines the field of attraction within the volume V. 

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