Integral representation for harmonic function in the ring is constructed in this work. We prove the existence and uniqueness of solutions of the Cauchy problem for the Laplace equation in the ring. Integral representation for the solution of the Cauchy problem was found.
Integral representations of separable states
Harmonic Functions and Riesz-Newtonian Potentials on 'Noisy' or Random Domains:Stochastic Extensions of Some Classical Theorems and Estimates
An Integro-Differential Equation of the Fractional Form: Cauchy Problem and Solution
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