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 boundsAnn. 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. EscauriazaNull-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. SincichSolving 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. SincichDetecting 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 bodiesInverse 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.