Geodesic
On Cauchy problem solution for a harmonic function in a simply connected domain
Problemy analiza, Tome 12 (2023) no. 2, pp. 87-96 Cet article a éte moissonné depuis la source Math-Net.Ru

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Here we present an investigation of the Cauchy problem solvability for the Laplace equation in a simply connected plane domain. The investigation is reduced to solution of two singular integral equations. If the problem is resolvable, its solution can be restored via the integral Cauchy formula. Examples of the solvable and unsolvable problems are presented. The construction involves the auxiliary approximate conformal mapping.
Keywords: Cauchy problem, integral equation, holomorphic function, spline, approximate solution. 
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E. A. Shirokova; P. N. Ivanshin. On Cauchy problem solution for a harmonic function in a simply connected domain. Problemy analiza, Tome 12 (2023) no. 2, pp. 87-96. http://geodesic.mathdoc.fr/item/PA_2023_12_2_a5/

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