VSP 2003 Parameter identi ̄ cation for Laplace equation and approximation in Hardy classes

| We consider the inverse problem of identifying a Robin coe± cient on some part of the boundary of a smooth 2D domain from overdetermined data available on the other part of the boundary, for Laplace equation in the domain. Using tools from complex analysis and analytic functions theory, we provide a constructive and convergent identi ̄cation scheme for this inverse problem, together with numerical experiments.

[1]  H. Begehr,et al.  Complex analytic methods for partial differential equations , 1996 .

[2]  Mohamed Jaoua,et al.  Un algorithme d'identification de frontières soumises à des conditions aux limites de Signorini , 2000 .

[3]  Michael V. Klibanov,et al.  A computational quasi-reversiblility method for Cauchy problems for Laplace's equation , 1991 .

[4]  Mohamed Jaoua,et al.  Identification of Robin coefficients by the means of boundary measurements , 1999 .

[5]  M. Zwaan.  An introduction to hilbert space , 1990 .

[6]  J. Partington,et al.  Hardy approximation to L 8 functions on subsets of the circle , 1996 .

[7]  Asymptotic Estimates for Interpolation and Constrained Approximation in $ H^{2} $ by Diagonalization of Toeplitz Operators , 2003 .

[8]  Mohamed Jaoua,et al.  Solution of the Cauchy problem using iterated Tikhonov regularization , 2001 .

[9]  Jonathan R. Partington,et al.  Problems of Adamjan—Arov—Krein Type on Subsets of the Circle and Minimal Norm Extensions , 2000 .

[10]  W. Rudin.  Real and complex analysis , 1968 .

[11]  P. Grisvard.  Boundary value problems in non-smooth domains , 1980 .

[12]  E. Saff,et al.  How can the meromorphic approximation help to solve some 2D inverse problems for the Laplacian , 1999 .

[13]  Jianxin Zhou,et al.  Boundary element methods , 1992, Computational mathematics and applications.

[14]  Dario Fasino,et al.  An inverse Robin problem for Laplace's equation: theoretical results and numerical methods , 1999 .

[15]  P. Duren.  Theory of H[p] spaces , 1970 .

[16]  F. Santosa,et al.  An effective nonlinear boundary condition for a corroding surface. Identification of the damage based on steady state electric data , 1998 .

[17]  J. Leblond,et al.  Hardy Approximation to L p Functions on Subsets of the Circle with 1• p <1 , 1998 .

[18]  L. Ahlfors.  Complex Analysis , 1979 .

[19]  G. Inglese,et al.  An inverse problem in corrosion detection , 1997 .

[20]  A constrained approximation problem arising in parameter identification , 2002 .

[21]  C. Pommerenke.  Boundary Behaviour of Conformal Maps , 1992 .