Abstract
In this paper, we consider the Cauchy problem for the Laplace operator. We construct approximate solutions by using the iterative method proposed by Bastay, Kozlov and Turesson. In the iterative method, we solve the corresponding boundary value problems repeatedly. Then, we show that we construct them more stably when we choose the smaller domain where we consider the boundary value problems. Furthermore, since the iterative method is applicable to the case where we know only approximations to the exact data with error, we also deal with this case.
Acknowledgments
The author expresses gratitude to Professor Sei Nagayasu (University of Hyogo) for many valuable discussions and comments. My deep appreciation goes to the anonymous referees for invaluable comments.
Citation
Akari Ishida. "A Depth-dependent Stability Estimate in an Iterative Method for Solving a Cauchy Problem for the Laplace Equation." Taiwanese J. Math. 27 (3) 577 - 609, June, 2023. https://doi.org/10.11650/tjm/230102
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