ON THE FIRST VARIATION OF THE SOLUTION TO BOUNDARY PROBLEMS IN THE THEORY OF THE POTENTIAL FOR THE VARIATION OF THE BOUNDARY SURFACE,
HONEYWELL INC ST PAUL MINN RESEARCH DEPT
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It is proved that the first variation of the solution to the boundary problem in potential theory is the linear functional operator on the function eta, which transforms the original surface, depending in a general case on the free member of the integral equation in the given boundary problem. The considerations are made in a general form for the exterior problem of Neumann. The simplifications obtained for the problem of Dirichlet will be evident. The course for the solution of the problem has been indicated by M. G. Krein.
- Theoretical Mathematics