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Thermomechanical modeling of energy-reaction-diffusion systems, including bulk-interface interactions
Estimating area of inclusions in anisotropic plates from boundary data
1. | Dipartimento di Ingegneria Civile e Architettura, Università degli Studi di Udine, via Cotonificio 114, 33100 Udine |
2. | Dipartimento di Matematica e Geoscienze, Università degli Studi di Trieste, via Valerio 12/1, 34127 Trieste, Italy |
3. | DIMAD, Università degli Studi di Firenze, via Lombroso 6/17, 50134 Firenze |
References:
[1] |
R. A. Adams, "Sobolev Spaces," Academic Press, New York, 1975. |
[2] |
G. Alessandrini, A. Morassi and E. Rosset, Size estimates, in "Inverse Problems: Theory and Applications" (eds. G. Alessandrini and G. Uhlmann), Contemp. Math., AMS, Providence, RI, 333 (2003), 33-75. |
[3] |
G. Alessandrini, A. Morassi and E. Rosset, Detecting an inclusion in an elastic body by boundary measurements, SIAM Rev., 46 (2004), 477-498.
doi: 10.1137/S0036144504442098. |
[4] |
G. Alessandrini, A. Morassi, E. Rosset and S. Vessella, On doubling inequalities for elliptic systems, J. Math. Anal. Appl., 357 (2009), 349-355.
doi: 10.1016/j.jmaa.2009.04.024. |
[5] |
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.
doi: 10.1137/S0036139996306468. |
[6] |
G. Alessandrini, L. Rondi, E. Rosset and S. Vessella, The stability for the Cauchy problem for elliptic equations, Inverse Problems, 25 (2009), 1-47.
doi: 10.1088/0266-5611/25/12/123004. |
[7] |
G. Alessandrini, E. Rosset and J. K. Seo, Optimal size estimates for the inverse conductivity problem with one measurement, Proc. Amer. Math. Soc., 128 (2000), 53-64.
doi: 10.1090/S0002-9939-99-05474-X. |
[8] |
S. Alinhac, Non-unicité pour des opérateurs différentiels à la caractéristiques complexes simples, Ann. Sci. École Norm. Sup., 13 (1980), 385-393. |
[9] |
M. Di Cristo, C. L. Lin and J. N. Wang, Quantitative uniqueness estimates for the shallow shell system and their application to an inverse problem, preprint (2011). |
[10] |
G. Fichera, Existence theorems in elasticity, in "Handbuch der Physik," VI, Springer-Verlag, Berlin (1972), 347-389. |
[11] |
M. E. Gurtin, The linear theory of elasticity, in "Handbuch der Physik," VI, Springer-Verlag, Berlin (1972), 1-295. |
[12] |
M. Ikehata, Size estimation of inclusion, J. Inverse Ill-Posed Probl., 6 (1998), 127-140. |
[13] |
H. Kang, J. K. Seo and D. Sheen, The inverse conductivity problem with one measurement: stability and estimation of size, SIAM J. Math. Anal., 28 (1997), 1389-1405.
doi: 10.1137/S0036141096299375. |
[14] |
Y. Lei, M. Di Cristo and G. Nakamura, Size estimates in thermography, Appl. Anal., 88 (2009), 831-46.
doi: 10.1080/00036810903042133. |
[15] |
A. Morassi and E. Rosset, Stable determination of cavities in elastic bodies, Inverse Problems, 20 (2004), 453-480.
doi: 10.1088/0266-5611/20/2/010. |
[16] |
A. Morassi, E. Rosset and S. Vessella, Size estimates for inclusions in an elastic plate by boundary measurements, Indiana Univ. Math. J., 56 (2007), 2325-2384.
doi: 10.1512/iumj.2007.56.2975. |
[17] |
A. Morassi, E. Rosset and S. Vessella, Detecting general inclusions in elastic plates, Inverse Problems, 25 (2009), Paper 045009.
doi: 10.1088/0266-5611/25/4/045009. |
[18] |
A. Morassi, E. Rosset and S. Vessella, Stable determination of a rigid inclusion in an anisotropic plate, preprint (2011), arXiv:math/1111.0604. |
[19] |
A. Morassi, E. Rosset and S. Vessella, Sharp three sphere inequality for perturbations of a product of two second order elliptic operators and stability for the Cauchy problem for the anisotropic plate equation, J. Funct. Anal., 261 (2011), 1494-1541.
doi: 10.1016/j.jfa.2011.05.011. |
show all references
References:
[1] |
R. A. Adams, "Sobolev Spaces," Academic Press, New York, 1975. |
[2] |
G. Alessandrini, A. Morassi and E. Rosset, Size estimates, in "Inverse Problems: Theory and Applications" (eds. G. Alessandrini and G. Uhlmann), Contemp. Math., AMS, Providence, RI, 333 (2003), 33-75. |
[3] |
G. Alessandrini, A. Morassi and E. Rosset, Detecting an inclusion in an elastic body by boundary measurements, SIAM Rev., 46 (2004), 477-498.
doi: 10.1137/S0036144504442098. |
[4] |
G. Alessandrini, A. Morassi, E. Rosset and S. Vessella, On doubling inequalities for elliptic systems, J. Math. Anal. Appl., 357 (2009), 349-355.
doi: 10.1016/j.jmaa.2009.04.024. |
[5] |
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.
doi: 10.1137/S0036139996306468. |
[6] |
G. Alessandrini, L. Rondi, E. Rosset and S. Vessella, The stability for the Cauchy problem for elliptic equations, Inverse Problems, 25 (2009), 1-47.
doi: 10.1088/0266-5611/25/12/123004. |
[7] |
G. Alessandrini, E. Rosset and J. K. Seo, Optimal size estimates for the inverse conductivity problem with one measurement, Proc. Amer. Math. Soc., 128 (2000), 53-64.
doi: 10.1090/S0002-9939-99-05474-X. |
[8] |
S. Alinhac, Non-unicité pour des opérateurs différentiels à la caractéristiques complexes simples, Ann. Sci. École Norm. Sup., 13 (1980), 385-393. |
[9] |
M. Di Cristo, C. L. Lin and J. N. Wang, Quantitative uniqueness estimates for the shallow shell system and their application to an inverse problem, preprint (2011). |
[10] |
G. Fichera, Existence theorems in elasticity, in "Handbuch der Physik," VI, Springer-Verlag, Berlin (1972), 347-389. |
[11] |
M. E. Gurtin, The linear theory of elasticity, in "Handbuch der Physik," VI, Springer-Verlag, Berlin (1972), 1-295. |
[12] |
M. Ikehata, Size estimation of inclusion, J. Inverse Ill-Posed Probl., 6 (1998), 127-140. |
[13] |
H. Kang, J. K. Seo and D. Sheen, The inverse conductivity problem with one measurement: stability and estimation of size, SIAM J. Math. Anal., 28 (1997), 1389-1405.
doi: 10.1137/S0036141096299375. |
[14] |
Y. Lei, M. Di Cristo and G. Nakamura, Size estimates in thermography, Appl. Anal., 88 (2009), 831-46.
doi: 10.1080/00036810903042133. |
[15] |
A. Morassi and E. Rosset, Stable determination of cavities in elastic bodies, Inverse Problems, 20 (2004), 453-480.
doi: 10.1088/0266-5611/20/2/010. |
[16] |
A. Morassi, E. Rosset and S. Vessella, Size estimates for inclusions in an elastic plate by boundary measurements, Indiana Univ. Math. J., 56 (2007), 2325-2384.
doi: 10.1512/iumj.2007.56.2975. |
[17] |
A. Morassi, E. Rosset and S. Vessella, Detecting general inclusions in elastic plates, Inverse Problems, 25 (2009), Paper 045009.
doi: 10.1088/0266-5611/25/4/045009. |
[18] |
A. Morassi, E. Rosset and S. Vessella, Stable determination of a rigid inclusion in an anisotropic plate, preprint (2011), arXiv:math/1111.0604. |
[19] |
A. Morassi, E. Rosset and S. Vessella, Sharp three sphere inequality for perturbations of a product of two second order elliptic operators and stability for the Cauchy problem for the anisotropic plate equation, J. Funct. Anal., 261 (2011), 1494-1541.
doi: 10.1016/j.jfa.2011.05.011. |
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