Bounds in the Cauchy problem for the Laplace equation
β Scribed by L. E. Payne
- Publisher
- Springer
- Year
- 1960
- Tongue
- English
- Weight
- 551 KB
- Volume
- 5
- Category
- Article
- ISSN
- 0003-9527
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π SIMILAR VOLUMES
We consider the Cauchy problem for the Laplace equation in the half plane x > 0 where the Cauchy data is given at x = 0 and the solution is sought in the interval 0 < x < 1. This is a model ill-posed problem since a small perturbation in the initial data leads to large errors in the solution. We use
The boundary value problem for the Laplace equation outside several cuts in a plane is studied. The jump of the solution of the Laplace equation and the jump of its normal derivative are specified of the cuts. The problem is studied under different conditions at infinity, which lead to different uni