Optimal stability for inverse elliptic boundary value problems with unknown boundaries
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 29 (2000) no. 4, pp. 755-806.
@article{ASNSP_2000_4_29_4_755_0,
     author = {Alessandrini, Giovanni and Beretta, Elena and Rosset, Edi and Vessella, Sergio},
     title = {Optimal stability for inverse elliptic boundary value problems with unknown boundaries},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     pages = {755--806},
     publisher = {Scuola normale superiore},
     volume = {Ser. 4, 29},
     number = {4},
     year = {2000},
     mrnumber = {1822407},
     zbl = {1034.35148},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_2000_4_29_4_755_0/}
}
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Alessandrini, Giovanni; Beretta, Elena; Rosset, Edi; Vessella, Sergio. Optimal stability for inverse elliptic boundary value problems with unknown boundaries. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 29 (2000) no. 4, pp. 755-806. http://www.numdam.org/item/ASNSP_2000_4_29_4_755_0/

[A-E] V. Adolfsson -L. Escauriaza, C1,α domains and unique continuation at the boundary, Comm. Pure Appl. Math. L (1997),935-969. | Zbl

[A-E-K] V. Adolfsson -L. Escauriaza -C. Kenig, Convex domains and unique continuation at the boundary, Rev. Mat. Iberoamericana 11 (1995), 513-525. | MR | Zbl

[Ag] S. Agmon, Unicité et convexité dans les problèmes differéntiels, Sém. de Mathématiques Sup. 13, Univ. de Montréal, 1965. | MR | Zbl

[Al1] G. Alessandrini, Stable determination of a crack from boundary measurements, Proc. Roy. Soc. Edinburgh 123 (1993), 497-516. | MR | Zbl

[Al2] G. Alessandrini, Examples of instability in inverse boundary-value problems, Inverse Problems 13 (1997), 887-897. | MR | Zbl

[Al-DiB] G. Alessandrini -E. Dibenedetto, Determining 2-dimensional cracks in 3-dimensional bodies: uniqueness and stability, Indiana Univ. Math. J. 46 (1997), 1-82. | MR | Zbl

[Al-R] G. Alessandrini -L. Rondi, Optimal stability for the inverse problem of multiple cavities, J. Differential Equations, to appear. | MR | Zbl

[Al-Ros] G. Alessandrini -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. | MR | Zbl

[Al-Ros-S] G. Alessandrini -E. Rosset -J.K. Seo, Optimal size estimatesfor the inverse conductivity problem with one measurement, Proc. Amer. Math. Soc., 128 (1999), 53-64. | MR | Zbl

[An-B-J] S. Andrieux -A. Ben Abda -M. Jaoua, Identifiabilité de frontière inaccessible par des mesures de surface, C. R. Acad. Sci. Paris 316 (1993), 429-434. | MR | Zbl

[B-K-W] H.T. Banks -F. Kojima -W.P. Winfree, Boundary estimation problems arising in thermal tomography, Inverse Problems 6 (1990), 897-921. | MR | Zbl

[Be-V] E. Beretta -S. Vessella, Stable determination of boundaries from Cauchy data, SIAM J. Math. Anal. 30 (1998), 220-232. | MR | Zbl

[Bi] A. Binder, On an inverse problem arising in continuous casting of steel billets, Appl. Anal. 57 (1995), 341-366. | MR | Zbl

[Br] R. Brummelhuis, Three-spheres theorem for second order elliptic equations, J. Anal. Math. 65 (1995), 179-206. | MR | Zbl

[Bu-C-Y1] A.L. Bukhgeim -J. Cheng -M. Yamamoto, Uniqueness and stabilily for an inverse problem of determining parts of boundary, in Inverse Problems in EngineeringMechanics, M. TANAKA, G.S. DULIKRAVICH (eds.), Elsevier, Amsterdam, 1998, 327-336. | MR

[Bu-C-Y2] A.L. Bukhgeim -J. Cheng -M. Yamamoto, On a sharp estimate in a nondestructive testing: determination of unknown boundaries, preprint, 1998. | MR

[Bu-C-Y3] A.L. Bukhgeim -J. Cheng -M. Yamamoto, Stability for an inverse boundary problem of determining a part of boundary, Inverse Problems 14 (1999), 1021-1032. | MR | Zbl

[Bu-C-Y4] A.L. Bukhgeim -J. Cheng -M. Yamamoto, Conditional stability in an inverse problem of determining non-smooth boundary, J. Math. Anal. Appl. 242 (2000), 57-74. | MR | Zbl

[C-F] R.R. Coifman -C.L. Fefferman, Weighted norm inequalities for maximal functions and singular integrals, Studia Math. 51 (1974), 241-250. | MR | Zbl

[F-V] A. Friedman -M. Vogelius, Determining cracks by boundary measurements, Indiana Univ. Math. J. 38 (1989), 527-556. | MR | Zbl

[G-L] N. Garofalo -F. Lin, Monotonicity properties of variational integrals, A p weights and unique continuation, Indiana Univ. Math. J. 35 (1986), 245-268. | MR | Zbl

[G-T] D. Gilbarg -N.S. Trudinger, "Elliptic partial differential equations of second order", Springer, New York, 1983. | MR | Zbl

[H] J. Hadamard, "Lectures on Cauchy's problem in linear partial differential equations", Dover, New York, 1953. | MR | Zbl

[K-S-V] P. Kaup -F. Santosa -M. Vogelius, A method for imaging corrosion damage in thin plates from electrostatic data, Inverse Problems 12 (1996), 279-293. | Zbl

[Ku] I. Kukavica, Quantitative uniqueness for second-order elliptic operators, Duke Math. J. 91 (1998), 225-240. | MR | Zbl

[Ku-N] I. Kukavica -K. Nyström, Unique continuation on the boundary for Dini domains, Proc. Amer. Math. Soc 126 (1998), 441-446. | MR | Zbl

[La] E.M. Landis, A three-sphere theorem, Dokl. Akad. Nauk SSSR 148 (1963), 277-279, Engl. trans. Soviet Math. Dokl. 4 (1963), 76-78. | MR | Zbl

[Li] G.M. Lieberman, Regularized distance and its applications, Pacific J. Math. 117 (1985), 329-353. | MR | Zbl

[M] K. Miller, Nonunique continuation for uniformly parabolic and elliptic equations in self-adjoint divergence form with Hölder continuous coefficients, Arch. Rational Mech. Anal. 54 (1974), 105-117. | MR | Zbl

[Pa1] L.E. Payne, Bounds in the Cauchy problem for the Laplace equation, Arch. Rational Mech. Anal. 5 (1960), 35-45. | MR | Zbl

[Pa2] L.E. Payne, On a priori bounds in the Cauchy problem for elliptic equations, SIAM J. Math. Anal. 1 (1970), 82-89. | MR | Zbl

[Pl] A Pliš, On non-uniqueness in Cauchy problem for an elliptic second order differential equation, Bull. Acad. Polon. Sci. 11 (1963), 95-100. | MR | Zbl

[Pu1] C. Pucci, Sui problemi di Cauchy non" ben posti", Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Nat. 18 (1955), 473-477. | MR | Zbl

[Pu2] C. Pucci, Discussione del problema di Cauchy per le equazioni di tipo ellittico, Ann. Mat. Pura Appl. 46 (1958), 131-153. | MR | Zbl

[R] L. Rondi, Optimal stability estimates for the determination of defects by electrostatic measurements, Inverse Problems 15 (1999), 1193-1212. | MR | Zbl

[T] G.N. Trytten, Pointwise bounds for solutions of the Cauchy problem for elliptic equations, Arch. Rational Mech. Anal. 13 (1963), 222-244. | MR | Zbl

[V1] S. Vessella, Stability estimates in an inverse problem for a three-dimensional heat equation, SIAM J. Math. Anal. 28 (1997), 1354-1370. | MR | Zbl

[V2] S. Vessella, Quantitative continuation from a measurable set of solutions of elliptic equation, Proc. Roy. Soc. Edinburgh Sect. A130(4) (2000), 909-923. | MR | Zbl