Abstract:
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.
Citation:
E. A. Shirokova, P. N. Ivanshin, “On Cauchy problem solution for a harmonic function in a simply connected domain”, Probl. Anal. Issues Anal., 12(30):2 (2023), 87–96
\Bibitem{ShiIva23}
\by E.~A.~Shirokova, P.~N.~Ivanshin
\paper On Cauchy problem solution for a harmonic function in a simply connected domain
\jour Probl. Anal. Issues Anal.
\yr 2023
\vol 12(30)
\issue 2
\pages 87--96
\mathnet{http://mi.mathnet.ru/pa377}
\crossref{https://doi.org/10.15393/j3.art.2023.12230}
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https://www.mathnet.ru/eng/pa377
https://www.mathnet.ru/eng/pa/v30/i2/p87
This publication is cited in the following 1 articles:
A. Darya, N. Taghizadeh, “On a boundary-value problem for the Poisson equation and the Cauchy–Riemann equation in a lens”, Probl. anal. Issues Anal., 14:1 (2025), 77–87
Citation in format AMSBIB
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