Published papers
103. G. Alessandrini,
V. Nesi, Globally
diffeomorphic $\sigma$--harmonic mappings Ann. Mat. Pura e Appl.
(2020), link to ArXiv.
102. G. Alessandrini,
A small collection of open problems, Rend. Istit.
Mat. Univ. Trieste Volume 52 (2020), 591-600, link
to ArXiv.
101. F. Faucher, G. Alessandrini,
H. Barucq, M. V. de Hoop, R. Gaburro,
E. Sincich , Full
reciprocity-gap waveform inversion enabling sparse-source acquisition, Geophysics
volume 85, issue 6 Nov 1, 2020.
100. G. Alessandrini,
V. Nesi, Breaking
through borders with $\sigma$--harmonic mappings, Le
Matematiche, Vol 75 No 1 (2020).
99. G. Alessandrini,
M. V. de Hoop, F. Faucher, R. Gaburro,
E. Sincich, Inverse
problem for the Helmholtz equation with Cauchy data: reconstruction with
conditional well-posedness driven iterative
regularization, ESAIM:
Mathematical Modelling and Numerical Analysis, 53, 3, May-June 2019, link to ArXiv.
98. G. Alessandrini, V. Nesi,
Locally invertible σ-harmonic mappings, Rend.
Mat. Appl. (7) 39 (2018) 195-203, link to ArXiv.
97. G. Alessandrini, E,
Rosset, S. Vessella, Optimal three spheres inequality at the boundary for the Kirchhoff-Love
plate's equation with Dirichlet conditions, Arch. Rational Mech. Anal.
March 2019, 231, (3), 1455–1486, link to ArXiv.
96. G. Alessandrini, M. V. de Hoop, R. Gaburro, E. Sincich, EIT in a layered anisotropic medium, Inverse Problems and Imaging,
2018 , 12, 3, 667-676. Link to ArXiv.
95. G. Alessandrini, M. V. de Hoop, R. Gaburro, E. Sincich, Lipschitz stability for a piecewise linear
Schrödinger potential from local Cauchy data (2017), Asymptotic
Analysis 108 (2018) 115–149. Link to ArXiv.
94. G. Alessandrini, M. V. de Hoop, R. Gaburro, Uniqueness
for the electrostatic inverse boundary value problem with piecewise constant
anisotropic conductivities, Inverse Problems 33 (2017) 125013. Link to ArXiv.
93. G. Alessandrini, A. Scapin,
Depth dependent resolution in Electrical
Impedance Tomography,(2017) J. Inv. Ill-Posed Problems 25(3), 391-402. Link to ArXiv.
92. G. Alessandrini, M. V. de Hoop, R. Gaburro, E. Sincich, Lipschitz stability for the electrostatic
inverse boundary value problem with piecewise linear conductivities (2016),
Journal de Mathématiques
Pures et Appliquées, 107 (5) 638–664. Link to ArXiv.
91. G. Alessandrini, M. Di Cristo, E. Francini, S. Vessella, Stability for quantitative photoacoustic
tomography with well-chosen illuminations, (2016), Ann. Mat. Pura e Appl., 2017, 196, (2) 395–406. Link to ArXiv.
90. G. Alessandrini,
V. Nesi, Quantitative
estimates on Jacobians for hybrid inverse problems, Bulletin of the South Ural State University.
Ser. Mathematical Modelling, Programming
& Computer Software (Bulletin SUSU MMCS), 2015, vol. 8, no. 3, pp.
25-41. Link to ArXiv.
89. G. Alessandrini,
A. Morassi, E. Rosset, S. Vessella, Global stability for an inverse problem in
soil-structure interaction, (2015) Proc. R. Soc. A 471: 20150117.
Link to ArXiv.
88. G. Alessandrini, V. Nesi, Estimates for the dilatation
of σ-harmonic mappings, Rendiconti
di Matematica e delle sue applicazioni 35 (3-4) (2014) 215-225. Link to ArXiv.
87. G. Alessandrini, Global stability for a coupled physics inverse problem, Inverse Problems 30 (2014)
075008, link to ArXiv.
86. G. Alessandrini, M. Di Cristo, A. Morassi, E. Rosset, Stable determination of an inclusion in an elastic body by boundary
measurements, SIAM J. Math. Anal., 46(4)
(2014) 2692–2729, link to ArXiv.
85. G. Alessandrini, E. Sincich,
Cracks with impedance, stable
determination from boundary data, Indiana Univ. Math. J. 62
(2013), 947-989, Newton
Institute preprint NI12054-INV.
84. G. Alessandrini, E. Sincich,
S. Vessella, Stable
determination of surface impedance on a rough obstacle by far field data, Inverse Problems and
Imaging 7, 2 (2013) 341-351, link to Arxiv.
83. G. Alessandrini, K. Kim, Single-logarithmic stability for the Calderón
problem with local data, J. Inv. Ill-Posed Problems 20,
4 (2012) Pages 389–400, link to Arxiv.
82. G. Alessandrini, Strong unique
continuation for general elliptic equations in 2D, J. Math. Anal. App. 386 (2012) 669–676, link to Arxiv.
81. G. Alessandrini, L. Rondi,
E. Rosset, S. Vessella, The stability for the
Cauchy problem for elliptic equations, Inverse Problems 25 123004,
2009, (47pp), link to Arxiv.
80. G. Alessandrini, R. Gaburro,
The local Calderòn problem and the determination
at the boundary of the conductivity, Comm. Partial Differential
Equations 34, (8), August 2009 , 918 - 936, link to Arxiv.
79. G. Alessandrini, A. Morassi,
E. Rosset, S. Vessella, On doubling inequalities
for elliptic systems, J. Math. Anal. App., 357, (2), 2009,
349-355, link to Arxiv.
78. G. Alessandrini, V. Nesi,
Invertible harmonic mappings, beyond Kneser,
Ann. Scuola Norm. Sup. Pisa, Cl. Sci. (5) VIII (2009), 451-468, link to Arxiv. Errata Corrige, Ann. Scuola Norm. Sup.
Pisa, Cl. Sci.(2) XVII (2017) 815-818.
77. G. Alessandrini, E. Cabib,
EIT and the average conductivity, J. Inv. Ill-Posed Problems
16, 8, 2008, 727–736, link to the preprint.
76. G. Alessandrini, V. Nesi,
Elliptic systems and material interpenetration, Funct. Approx.
Comment. Math., 40 ( 1), 2009, 105-115, link to Arxiv.
75. G. Alessandrini, V. Nesi,
Beltrami operators,
non-symmetric elliptic equations and quantitative Jacobian bounds, Ann. Acad. Sci. Fenn. Math. 34, 2009,
47-67.
74. G. Alessandrini, E. Rosset, Symmetry of
singular solutions of degenerate quasilinear elliptic equations, Rend. Istit. Mat. Univ. Trieste 39 (2007), 1-8.
73. G. Alessandrini, A. Morassi,
E. Rosset, The linear constraints in Poincare’ and Korn type inequalities,
Forum Mathematicum 28 (3) 2008, 557–569.
72. G. Alessandrini, Open issues of
stability for the inverse conductivity problem, J. Inv. Ill-Posed Problems 15 (5) 2007,
451-460.
71. G. Alessandrini, L. Escauriaza, Null-controllability
of one-dimensional parabolic equations, ESAIM: COCV 14 2 (2008)
284-293
70. G. Alessandrini, A. Bilotta,
A. Morassi, E. Rosset , E. Turco, Computing Volume
Bounds of Inclusions by EIT Measurements, J. Sci.
Comp.33, Number 3 / December, 2007.
69. G. Alessandrini, E. Cabib,
Determining the anisotropic traction state in a membrane by boundary measurements, Inverse Problems and
Imaging 1 (3) August 2007, 437-442.
68. G. Alessandrini, E. Sincich, Solving
elliptic Cauchy problems and the identification of nonlinear corrosion,
J. Comput.
Appl. Math 198
(2) January 2007, 307-320 Applied Computational
Inverse Problems.
67. G. Alessandrini, A. Bilotta,
G. Formica, A. Morassi, E. Rosset ,
E. Turco, Evaluating the volume of a hidden inclusion in an elastic body,
J. Comput.
Appl. Math 198 (2) January 2007, 288-306
Applied Computational Inverse Problems.
66. G. Alessandrini, E. Sincich, Detecting
nonlinear corrosion by electrostatic measurements, Applicable
Anal. 85, 1–3, January–March 2006, 107–128.
65. G. Alessandrini, M. Di Cristo, Stable
determination of an inclusion by boundary measurements, SIAM J. Math. Anal. 37 (1)
(2005) 200-217.
64. G. Alessandrini, S. Vessella,
Lipschitz Stability for the Inverse Conductivity Problem, Adv. Appl. Math. 35, 2 (August 2005) 207-241.
63. G. Alessandrini, A. Bilotta,
G. Formica, A. Morassi, E. Rosset ,
E. Turco, Numerical size estimates of inclusions in elastic bodies,
Inverse
Problems 21 (February 2005) 133-151.
62. G. Alessandrini, A. Morassi,
E. Rosset, Detecting an inclusion in
an elastic body by boundary measurements, SIAM Review 46 (3) (2004) 477 - 498.
(revised and updated version of [52]).
61. G. Alessandrini, L. Rondi,
Determining a sound-soft polyhedral scatterer by a
single far-field measurement,
Proc. Amer.
Math. Soc. 133 (2005), 1685-1691. Corrigendum: Determining a sound-soft polyhedral scatterer by a single far-field measurement, link to ArXiv.
60. G. Alessandrini, E. Rosset,
Volume bounds of inclusions from physical EIT
measurements, Inverse Problems 20
(April 2004) 575-588 .
59. G. Alessandrini , L. Del Piero, L. Rondi, Stable determination of corrosion by a single
electrostatic boundary measurement, Inverse
Problems 19 (August 2003) 973-984.
58. G. Alessandrini, S. Vessella,
Remark on the strong unique continuation property for parabolic operators,
Proc. Amer.
Math. Soc. 132 (2004), 499-501.
57. G. Alessandrini, A. Morassi,
E. Rosset, Size estimates , in: G. Alessandrini,
G. Uhlmann eds., Inverse Problems: Theory and Applications, Contemporary
Mathematics vol. 333 American Mathematical Society 2003 .
56. G. Alessandrini, A. Morassi,
E. Rosset, Detecting cavities by electrostatic boundary measurements,
Inverse
Problems 18 ( 2002)1333-1353
.
55. G. Alessandrini, V. Nesi,
Univalent σ-harmonic mappings: connections with quasiconformal mappings , J. Analyse Math.. 90 (2003)
197-215.
54. G. Alessandrini, V. Nesi,
Area formulas for σ-harmonic mappings , in: M.Sh. Birman, S. Hildebrandt, V.A. Solonnikov,
N.N. Uraltseva eds., Nonlinear Problems in
Mathematical Physics and Related Topics I, In Honor
of Professor O. A. Ladyzhenskaya, Kluwer
Academic/Plenum Publishers and Tamara Rozhkoskaya
(Russian edition), 2002.
53. G. Alessandrini, V. Nesi,
Univalent σ-harmonic mappings: applications to
composites , ESAIM: COCV,
June 2002, Vol. 7, pp. 379-406.
52. G. Alessandrini, A. Morassi,
E. Rosset, Detecting an inclusion in
an elastic body by boundary measurements, SIAM J. Math. Anal. 33, (6)(2002)
1247-1268.
51. G. Alessandrini, A. Morassi,
Strong unique continuation for the Lamé system of
elasticity, Comm. Partial Differential
Equations 26 (9&10) (2001) 1787-1810.
50. G. Alessandrini, R. Gaburro,
Determining conductivity with special anisotropy by boundary
measurements, SIAM J. Math. Anal. 33 (1)
(2001) 153-171.
49. G. Alessandrini, L. Rondi,
Optimal stability for the inverse problem of multiple cavities, Journal of Differential
Equations 176 (2001) 356 –386.
48. G. Alessandrini, V. Nesi,
Univalent σ-harmonic mappings, Arch.
Rational Mech. Anal. 158 (2001) 2, 155-171 .
47. G. Alessandrini, E. Beretta, E. Rosset, S. Vessella, Inverse boundary value problems with unknown boundaries: optimal stability, Comptes
Rendus Acad. Sci. Paris 328 Ser.
IIb Mécanique (2000) 607-611.
46. G. Alessandrini, E. Beretta, E. Rosset, S. Vessella, Optimal stability for inverse elliptic
boundary value problems with unknown boundary, Ann. Scuola Norm. Sup. Pisa, Cl. Sci.(4) XXIX(2001) 755-806..
45. G. Alessandrini, M. Sigalotti,
Geometric properties of solutions to the anisotropic p-Laplace equation in
dimension two, Ann. Acad.
Sci. Fenn. Math. 21 (2001) 249-266 .
44. G. Alessandrini, A.Favaron, Sharp stability estimates of harmonic
continuation along lines, Math.
Methods Appl. Sci. 23(12) 2000, 1037-1056.
43. G. Alessandrini, M. Di Cristo, Unique
determination of surface breaking cracks in three dimensional bodies, J.
Inverse Ill-Posed Probl. 8 (5) (2000) 469-482.
42. G .Alessandrini, E. Rosset, J.K. Seo, Optimal size estimates for the inverse conductivity
problem with one measurement, Proc. Amer.
Math. Soc. 128 (2000), 53-64.
41. G. Alessandrini, Generic uniqueness and size
estimates in the inverse conductivity problem with one measurement , in International Conference
on Boundary Value Problems For Elliptic And Parabolic Operators, In memory of
Filippo Chiarenza , Catania 1998. Le Matematiche LIV (1999) Supplemento,
5-14.
40. G. Alessandrini, L.Rondi, Stable determination of a crack in a
planar inhomogeneous conductor, SIAM J. Math. Anal. 30 (2)(1998) 326-340.
39. G. Alessandrini, E. Rosset, The
inverse conductivity problem with one measurement: bounds on the size of the
unknown object ,
SIAM J.Appl.
Math.58 (4)(1998) 1060-1071.
38. G. Alessandrini, R. Magnanini,
Symmetry and non-symmetry in some overdetermined boundary value problems , in G.Caristi, E.Mitidieri, Reaction Diffusion Systems, M.Dekker, New York, 1997, 1-12.
37. G. Alessandrini, Examples of
instability in inverse boundary value problems, Inverse
Problems 13 (1997) 887-897.
36. G. Alessandrini, E. DiBenedetto, Determining
2-dimensional cracks in 3-dimensional bodies: uniqueness and stability, Indiana Univ. Math. J., 46
(1) (1997) 1-82.
35. G. Alessandrini, V. Isakov, Analyticity
and uniqueness for the inverse conductivity problem, Rend. Istit.
Mat. Univ.Trieste 28 (I&II) (1996)
351-370.
34. G. Alessandrini, On Courant's nodal
domain theorem, Forum Mathematicum 10 (1998) 521-532.
33. G. Alessandrini, A. Diaz Valenzuela, Unique
determination of multiple cracks by two measurements, SIAM J. Control Optim. 34 (3) (1996) 913-921.
32. G. Alessandrini, E. Beretta e S. Vessella, Determining linear cracks by boundary
measurements: Lipschitz stability, SIAM J. Math. Anal. 27
(2) (1996) 361-375.
31. G. Alessandrini, R. Magnanini,
Symmetry and non-symmetry for the overdetermined Stekloff
eigenvalue problem II, in L. P. Cook, T. S. Angell, R. E. Kleinmann, W. E. Olmstead editori,
Nonlinear Boundary Value Problems, SIAM Philadelphia, 1995. Link to the
preprint.
30. G. Alessandrini, E. Beretta, F. Santosa e S. Vessella, Stability
in crack determination from electrostatic measurements at the boundary. A
numerical investigation, Inverse
Problems, 11 (1995) L17-L24.
29. G. Alessandrini, V. Isakov e J. Powell,
Local uniqueness in the inverse conductivity problem with one measurement,
Trans. Amer. Math. Soc. 347, 8
(1995), 3031-3041.
28. G. Alessandrini, R. Magnanini,
Elliptic equations in divergence form, geometric critical points of
solutions and Stekloff eigenfunctions, SIAM J. Math. Anal., 25 (5)
(1994), 1259-1268.
27. G. Alessandrini, Nodal lines of
eigenfunctions of the fixed membrane problem in general convex domains, Commentarii Math. Helvetici, 69
(1994), 142-154.
26. G. Alessandrini, R. Magnanini,
Symmetry and non-symmetry for the overdetermined Stekloff
eigenvalue problem, ZAMP 45 1 (1994) 4452.
25. G. Alessandrini, D. Lupo,
E. Rosset, Local behavior and geometric properties
of solutions to degenerate quasilinear elliptic equations in the plane, Applicable Anal., 50 (1993)
191-215.
24. G. Alessandrini, R. Magnanini,
The index of isolated critical points and solutions of elliptic equations in
the plane, Ann. Scuola
Norm. Sup. Pisa, Cl. Sci. (4) XIX 4 (1992) 567-589.
23. G. Alessandrini, Stability for the
crack determination problem, in L. Paivarinta e E. Somersalo, Inverse Problems in
Mathematical Physics, 1993, Springer, Berlin, 18.
22. G. Alessandrini, Stable determination
of a crack from boundary measurements, Proc. Royal Soc. Edinburgh Ser., A
127 (3) (1993) 497-516.
21. G. Alessandrini, A symmetry theorem
for condensers, Math. Meth.
Appl. Sci., 15 (1992), 315-320.
20. G. Alessandrini, Determining
conductivity by boundary measurements, the stability issue, in R.Spigler, Applied and
Industrial Mathematics, Kluwer 1991.
19. G. Alessandrini, Isoperimetric
inequalities for the length of level lines of solutions of quasilinear capacity
problems in the plane, ZAMP, 40 (1989), 920-924.
18. G. Alessandrini, Characterizing
spheres by functional relations on solutions of elliptic and parabolic
equations, Applicable
Anal., 40 (1991), 251-261.
17. G. Alessandrini, Matzoh ball soup: a
symmetry result for the heat equation, J. Analyse Math., 54 (1990),
229-236.
16. G. Alessandrini, J. Sylvester, Stability
for a multidimensional inverse spectral theorem, Comm. Partial Differential
Equations, 15(5) (1990), 711-736.
15. G. Alessandrini, N. Garofalo, Symmetry
for degenerate parabolic equations, Arch. Rat. Mech. Anal., 108 (2)
(1989), 161-174.
14. G. Alessandrini, Singular solutions
of elliptic equations and the determination of conductivity by boundary
measurements, J. Differential Equations 84
(2) (1990), 252-272.
13. G. Alessandrini, Remark on a paper
by Bellout and Friedman, Boll. Un. Mat. Ital., A
(7) 3 (1989), 243-249.
12. G. Alessandrini, Stable
determination of conductivity by boundary measurements, Applicable Anal., 27
(1988), 153-172.
11. G. Alessandrini, S. Vessella,
Local behaviour of solutions to parabolic equations, Comm. Partial Differential
Equations, 13 (9) ,
(1988), 153-172.
10. G. Alessandrini, The length of level
lines of solutions of elliptic equations in the plane, Arch. Rat. Mech.
Anal., 102 (2) ,
(1988), 183-1916.
9. G. Alessandrini, Critical points of
solutions to the p-Laplace equation in dimension two, Boll. Un. Mat. Ital.,
A (7) 1 (1987), 239-246.
8. G. Alessandrini, Critical points of solutions
of elliptic equations in two variables, Ann. Scuola Norm. Sup. Pisa Cl. Sci., (4) XIV 2 (1987), 229-256.
7. G. Alessandrini, An identification problem for
an elliptic equation in two variables, Ann. Mat. Pura e Appl., 4 (1986),
265-296.
6. G. Alessandrini, S. Vessella,
Error estimates in an identification problem for a parabolic equation,
Boll. Un. Mat. Ital. C(6) 4
(1985),183-203.
5. G. Alessandrini, On the identification of
the leading coefficient of an elliptic equation, Boll. Un. Mat. Ital. C(6) 4 (1985), 87-111.
4. G. Alessandrini, A. Douglis,
E. Fabes, An approximate layering method for the Navier Stokes equation in bounded cylinders, Ann. Mat.
Pura Appl. (4) 135 (1983), 239-348.
3. G. Alessandrini, On elliptic equations with
an axial symmetry, Ann. Mat. Pura Appl. (4) 127 (1981), 365-381.
2. G. Alessandrini, On
differentiation of approximately given functions, Applicable Anal. 11 1
(1980/81), 45-59.
1. G. Alessandrini, An extrapolation problem
for harmonic functions, Boll. Un. Mat. Ital., B (5) 17 (1980),
860-875.
Conference proceedings
1. G. Alessandrini, An identification problem for
an elliptic equation in two variables, in P.C. Sabatier, Problemes
Inverses, Université des Sciences et Techniques
Languedoc, Montpellier, 1986, 1-5.
2. G. Alessandrini, E. Rosset, Efficient
detection of an inclusion in a conductor, in I.Troch, F.Breitenecher,
2nd MathMod Vienna Proceedings , Argesim,
Vienna, 1997, 1015-1020.
Past Preprints
1. G. Alessandrini, Some remarks on a problem of
sound measurements from incomplete data, Berichte der Arbeitsgruppe Technomathematik,
Universitat Kaiserslautern, 17 (1985), 1-28.
2. G. Alessandrini, A simple proof of the unique
continuation property for two dimensional elliptic equations in divergence form,
Quaderni Matematici II serie,
276 Agosto 1992, Dipartimento di Scienze
Matematiche, Trieste.
3. G. Alessandrini, V. Nesi,
Univalence of σ-harmonic mappings and applications, Newton Institute preprint
NI00006-SMM.