ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

15. Numerical Analysis and Scientific Computing

1991 MS Classification: 35, 47, 65 Leitão, Antonio, Dep. of Mathematics, Federal Univ. of Santa Catarina, Brasil On a Linear Operator Related to the Solution of Elliptic Cauchy Problems The algorithm of Maz’ia et al. [Ma] for solving linear elliptic Cauchy problems of second order is formulated in [Le] for general elliptic operators with C^{∞}-coefficients. A new convergence proof for this iterative algorithm using a functional analytical approach is given in [Le], where the iteration is described using powers of an affine operator T. We discuss here other properties of T_{l} (the linear part of T) such as positiveness, self adjointness and injectivity. The effectiveness of two regularization schemas based on the spectral decomposition of T_{l} is also considered.

[Le] A. Leitão, An Iterative Method for Solving linear and some non linear elliptic Cauchy Problems, to appear in SIAM J. of [Ma] V. A. Kozlov, V. G. Maz’ya und A. V. Fomin, An iterative method for solving the Cauchy problem for elliptic equations Comput. Maths. Phys., Vol. 31, No. 1 (1991), 45–52.