- V. Adolfsson and L. Escauriaza, C1,α domains and unique continuation at the boundary. Comm. Pure Appl. Math. L (1997) 935-969.
- G. Alessandrini and E. Rosset, The inverse conductivity problem with one measurement: Bounds on the size of the unknown object. SIAM J. Appl. Math. 58 (1998) 1060-1071. [CrossRef] [MathSciNet]
- G. Alessandrini and L. Rondi, Optimal stability for the inverse problem of multiple cavities. J. Differential Equations 176 (2001) 356-386. [CrossRef] [MathSciNet]
- G. Alessandrini, E. Beretta, E. Rosset and S. Vessella, Optimal stability for inverse elliptic boundary value problems with unknown boundaries. Ann. Scuola Norm. Sup. Pisa Cl. Sci (4) XXIX (2000) 755-806.
- K. Bryan and L.F. Candill Jr., An inverse problem in thermal imaging. SIAM J. Appl. Math. 56 (1996) 715-735. [CrossRef] [MathSciNet]
- K. Bryan and L.F. Candill Jr., Uniqueness for boundary identification problem in thermal imaging, in Differential Equations and Computational Simulations III, edited by J. Graef, R. Shivaji, B. Soni and J. Zhu.
- K. Bryan and L.F. Candill Jr., Stability and reconstruction for an inverse problem for the heat equation. Inverse Problems 14 (1998) 1429-1453. [CrossRef] [MathSciNet]
- B. Canuto, E. Rosset and S. Vessella, Quantitative estimates of unique continuation for parabolic equations and inverse initial-boundary value problems with unknown boundaries. Trans. AMS 354 (2002) 491-535. [CrossRef]
- R. Courant and D. Hilbert, Methods of Mathematical Physics, Vol. 1. Wiley, New York (1953).
- D. Gilbarg and N.S. Trudinger, Elliptic partial differential equations of second order. Springer, New York (1983).
- V. Isakov, Inverse problems for partial differential equations. Springer, New York (1998).
- S. Ito and H. Yamabe, A unique continuation theorem for solutions of a parabolic differential equation. J. Math. Soc. Japan 10 (1958) 314-321. [CrossRef] [MathSciNet]
- O.A. Ladyzhenskaja, V.A. Solonnikov and N.N. Ural'ceva, Linear and quasilinear equations of parabolic type. Amer. Math. Soc., Providende, Math. Monographs 23 (1968).
- E.M. Landis and O.A. Oleinik, Generalized analyticity and some related properties of solutions of elliptic and parabolic equations. Russ. Math. Surveys 29 (1974) 195-212. [CrossRef]
- F.H. Lin, A uniqueness theorem for parabolic equations. Comm. Pure Appl. Math. XLIII (1990) 127-136.
- J.L. Lions and E. Magenes, Non-homogeneous boundary value problems and applications II. Springer, New York (1972).
- A. Pazy, Semigroups of linear operators and applications to partial differential equations. Springer, New York (1983).
- S. Vessella, Stability estimates in an inverse problem for a three-dimensional heat equation. SIAM J. Math. Anal. 28 (1997) 1354-1370. [CrossRef] [MathSciNet]
Volume 7, 2002
|Page(s)||521 - 565|
|Published online||15 September 2002|