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FOUNDATIONS OF POTENTIAL THEORY
Greens Formula and Its Consequences
Investigation of Boundary Problems by
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analogous analytic angle arbitrary constants assumes the form auxiliary problem boundary condition bounded circle closed domain coefficients conjugate harmonic functions consider construct continuously differentiable coordinates curve of contact defined denote direction Dirichlet problem disk equal to zero extremal curve finite number follows formula Fredholm equation function F gradient Green's formula Green's function half-space H harmonic polynomial Holder condition Holder continuous holomorphic homogeneous equation homogeneous problem corresponding increment independent variables inhomogeneous intersection investigate kernel Laplace's equation Let us assume linearly independent linearly independent solutions manifold neighborhood Neumann problem oblique derivative problem Obviously operator Oz axis point of domain point Xo polynomial potential problem for harmonic regular harmonic functions regular in ball regular in domain respect rotation satisfies a Holder satisfies the condition single-valued singular points smooth solvable sphere sufficiently small surface tangent plane tends to zero Theorem tion unique values vanish vector field