Determining the anisotropic traction state in a membrane by boundary measurements

Inverse Problems and Imaging

Volumn 1, Issue 3, 2007, Pages 437-442

  Alessandrini, Giovanni ^a   Cabib, Elio ^b  

^a UNIVERSITY OF TRIESTE   (Italy)

^b UNIVERSITY OF UDINE   (Italy)

Author keywords

Anisotropy; Inverse boundary problems; Prestressed membranes

Indexed keywords

EID: 80051985075     PISSN: 19308337     EISSN: 19308345     Source Type: Journal    
DOI: 10.3934/ipi.2007.1.437     Document Type: Article

References (18)

1. L. V. Ahlfors, “Lectures on quasiconformal mappings,” Van Nostrand Mathematical Studies, 10, Van Nostrand, Toronto, 1966.
2. G. Alessandrini, Stable determination of conductivity by boundary measurements, Appl. Anal., 27 (1988), 153–172.
3. G. Alessandrini and S. Vessella, Lipschitz stability for the inverse conductivity problem, Advances Appl. Math., 35 (2005), 207–241.
4. K. Astala and L. Päivärinta, M. Lassas, Calderón’s inverse problem for anisotropic conductivity in the plane, Comm. Partial Differential Equations, 30 (2005), 207–224.
5. K. Astala and L. Päivärinta, Calderón’s inverse conductivity problem in the plane, Ann. of Math., 2 163 (2006), 265–299.
6. E. Cabib, C. Davini and C.-Q. Ru, A problem in the optimal design of networks under transverse loading, Quart. Appl. Math., 48 (1990), 251–263.
7. E. Cabib and C. Davini, On the variational convergence with a null divergence condition, Boll. Un. Mat. Ital., (7) 5-B (1991), 171–176.
8. A. P. Calderón, On an inverse boundary value problem, Seminar on Numerical Analysis and its Applications to Continuum Physics, Rio de Janeiro, 1980, Soc. Brasil. Mat., Rio de Janeiro, 1980, 65–73.
9. G. Dal Maso, “An Introduction to Γ-convergence,” Birkhäuser, Boston, 1993.
10. E. De Giorgi and S. Spagnolo, Sulla convergenza degli integrali dell’energia per operatori ellittici del secondo ordine, Boll. Un. Mat. Ital., 8 (1973), 391–411.
11. R. Kohn and M. Vogelius, Identification of an unknown conductivity by means of measure- ments at the boundary, Inverse Problems, edited by D. McLaughlin, SIAM-AMS Proceedings, 14 (1984), 113–123.
12. R. Kohn and M. Vogelius, Relaxation of a variational method for impedance computed tomography, Comm. Pure Appl. Math., 40 (1987), 745–777.
13. A. Marino and S. Spagnolo, Un tipo di approssimazione dell’operatore (formula presented) con operatori (formula presented), Ann. Scuola Norm. Sup. Pisa (3), 23 (1969), 657–673.
14. A. I. Nachman, Global uniqueness for a two-dimensional inverse boundary value problem, Ann. of Math. (2), 143 (1996), 71-96.
15. G. Nakamura and G. Uhlmann, Global uniqueness for an inverse boundary value problem arising in elasticity, Invent. Math., 118 (1994), 457–474.
16. S. Spagnolo, Sulla convergenza di soluzioni di equazioni paraboliche ed ellittiche, Ann. Scuola Norm. Sup. Pisa, 22 (1968), 571-597.
17. S. Spagnolo, Convergence in energy for elliptic operators, in “Numerical Solutions of Partial Differential Equations - III” (SYNSPADE 1975), vol. 1, College Park (Maryland) 1976, 469–498.
18. J. Sylvester, An anisotropic inverse boundary value problem, Comm. Pure Appl. Math., 43 (1990), 201–232.