Abstract
The paper investigates the stability of the Cauchy problem for the Laplace equation under the a priori assumption that the solution is bounded. A special metrization of the weak topology in the space L2 and the standard Fourier series technique are applied to obtain stability bounds for the solution of the Cauchy problem on the class of absolutely bounded functions.
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Additional information
Translated from Vychislitel'naya Matematika i Matematicheskoe Obespechenie EVM, pp. 44–50, 1985.
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Gaponenko, Y.L. Stability of the solution of the Cauchy problem for the Laplace equation on a weak compactum. Comput Math Model 1, 23–27 (1990). https://doi.org/10.1007/BF01128306
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DOI: https://doi.org/10.1007/BF01128306