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The Neumann problem in a plane domain bounded by closed and open curves. (English) Zbl 0982.31001

The Neumann problem for the Laplace equation in a connected plane region bounded by closed and open curves is studied. The existence of a classical solution is proved by potential theory. The problem is reduced to a Fredholm equation of the second kind, which is uniquely solvable.

MSC:

31A10 Integral representations, integral operators, integral equations methods in two dimensions
31A05 Harmonic, subharmonic, superharmonic functions in two dimensions
35J25 Boundary value problems for second-order elliptic equations
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