Giovanni Alessandrini

Published papers

  1. G. Alessandrini, An extrapolation problem for harmonic functions, Boll. Un. Mat. Ital., B (5) 17 (1980), 860-875.
  2. G. Alessandrini, On differentiation of approximately given functions, Applicable Anal. 11 1 (1980/81), 45-59.
  3. G. Alessandrini, On elliptic equations with an axial symmetry , Ann. Mat. Pura Appl. (4) 127 (1981), 365-381.
  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.
  5. G. Alessandrini, On the identification of the leading coefficient of an elliptic equation, Boll. Un. Mat. Ital. C(6) 4 (1985), 87-111.
  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.
  7. G. Alessandrini, An identification problem for an elliptic equation in two variables, Ann. Mat. Pura e Appl., 4 (1986), 265-296.
  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.
  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.
  10. G. Alessandrini, The length of level lines of solutions of elliptic equations in the plane, Arch. Rat. Mech. Anal., 102 (2) , (1988), 183-191.
  11. G. Alessandrini, S. Vessella, Local behaviour of solutions to parabolic equations, Comm. Partial Differential Equations, 13 (9) , (1988), 153-172.
  12. G. Alessandrini, Stable determination of conductivity by boundary measurements, Applicable Anal., 27 (1988), 153-172.
  13. G. Alessandrini, Remark on a paper by Bellout and Friedman, Boll. Un. Mat. Ital., A (7) 3 (1989), 243-249.
  14. G. Alessandrini, Singular solutions of elliptic equations and the determination of conductivity by boundary measurements, J. Differential Equations 84 (2) (1990), 252-272.
  15. G. Alessandrini, N. Garofalo, Symmetry for degenerate parabolic equations, Arch. Rat. Mech. Anal., 108 (2) (1989), 161-174.
  16. G. Alessandrini, J. Sylvester, Stability for a multidimensional inverse spectral theorem, Comm. Partial Differential Equations, 15(5) (1990), 711-736.
  17. G. Alessandrini, Matzoh ball soup: a symmetry result for the heat equation, J. Analyse Math., 54 (1990), 229-236.
  18. G. Alessandrini, Characterizing spheres by functional relations on solutions of elliptic and parabolic equations, Applicable Anal., 40 (1991), 251-261.
  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.
  20. G. Alessandrini, Determining conductivity by boundary measurements, the stability issue, in R.Spigler, Applied and Industrial Mathematics, Kluwer 1991.
  21. G. Alessandrini, A symmetry theorem for condensers, Math. Meth. Appl. Sci., 15 (1992), 315-320.
  22. G. Alessandrini, Stable determination of a crack from boundary measurements, Proc. Royal Soc. Edinburgh Ser., A 127 (3) (1993) 497-516.
  23. G. Alessandrini, Stability for the crack determination problem, in L. Paivarinta e E. Somersalo, Inverse Problems in Mathematical Physics, 1993, Springer, Berlin, 18.
  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.
  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.
  26. G. Alessandrini, R. Magnanini, Symmetry and non-symmetry for the overdetermined Stekloff eigenvalue problem, ZAMP 45 1 (1994) 4452.
  27. G. Alessandrini, Nodal lines of eigenfunctions of the fixed membrane problem in general convex domains, Commentarii Math. Helvetici, 69 (1994), 142-154.
  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.
  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.
  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.
  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.
  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.
  33. G. Alessandrini, A. Diaz Valenzuela, Unique determination of multiple cracks by two measurements, SIAM J. Control Optim. 34 (3) (1996) 913-921.
  34. G. Alessandrini, On Courant's nodal domain theorem, Forum Mathematicum 10 (1998) 521-532.
  35. G. Alessandrini, V. Isakov, Analyticity and uniqueness for the inverse conductivity problem, Rend. Istit. Mat. Univ.Trieste 28 (I&II) (1996) 351-370.
  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.
  37. G.Alessandrini, Examples of instability in inverse boundary value problems, Inverse Problems 13 (1997) 887-897.
  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.
  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.
  40. G. Alessandrini, L.Rondi, Stable determination of a crack in a planar inhomogeneous conductor, SIAM J. Math. Anal. 30 (2)(1998) 326-340.
  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.
  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.
  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.
  44. G.Alessandrini, A.Favaron, Sharp stability estimates of harmonic continuation along lines,   Math. Methods Appl. Sci. 23(12) 2000, 1037-1056.
  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 .
  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..
  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.
  48. G.Alessandrini, V.Nesi, Univalent s -harmonic mappings, Arch. Rational Mech. Anal. 158 (2001) 2, 155-171 .
  49. G.Alessandrini, L.Rondi, Optimal stability for the inverse problem of multiple cavities, Journal of Differential Equations 176 (2001) 356 –386.
  50. G.Alessandrini, R.Gaburro, Determining conductivity with special anisotropy by boundary measurements,  SIAM J. Math. Anal. 33 (1) (2001) 153-171.
  51. G.Alessandrini, A.Morassi, Strong unique continuation for the Lamé system of elasticity, Comm. Partial Differential Equations 26 (9&10) (2001) 1787-1810.
  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.
  53. G.Alessandrini, V.Nesi, Univalent  s-harmonic mappings: applications to composites , ESAIM: COCV, June 2002, Vol. 7, pp. 379-406.
  54. G.Alessandrini, V.Nesi, Area formulas for s-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. 
  55. G.Alessandrini, V.Nesi, Univalent s-harmonic mappings: connections with quasiconformal mappings , J. Analyse Math.. 90 (2003) 197-215.
  56. G.Alessandrini, A.Morassi, E.Rosset,  Detecting cavities by electrostatic boundary measurements, Inverse Problems 18 ( 2002)1333-1353 .
  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 .
  58. G.Alessandrini, S.Vessella, Remark on the strong unique continuation property for parabolic operators, Proc. Amer. Math. Soc. 132 (2004), 499-501.
  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.
  60. G. Alessandrini, E. Rosset,  Volume bounds of inclusions from physical EIT measurements, Inverse Problems 20 (April 2004) 575-588 .  
  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
  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 [50]).
  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.
  64. G. Alessandrini, S. Vessella, Lipschitz Stability for the Inverse Conductivity Problem, Adv. Appl. Math. 35,  2 (August 2005) 207-241.
  65. G.Alessandrini, M. Di Cristo, Stable determination of an inclusion by boundary measurements, SIAM J. Math. Anal. 37 (1) (2005) 200-217.
  66. G. Alessandrini, E. Sincich,  Detecting nonlinear corrosion by electrostatic measurements, Applicable Anal. 85, 1–3, January–March 2006, 107–128.
  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.
  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.
  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.
  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.
  71. G.Alessandrini, L. Escauriaza,  Null-controllability of one-dimensional parabolic equations, ESAIM: COCV 14 2 (2008) 284-293
  72. G. Alessandrini, Open issues of stability for the inverse conductivity problem, J. Inv. Ill-Posed Problems 15 (5) 2007, 451-460.
  73. G.Alessandrini, A.Morassi, E.Rosset, The linear constraints in Poincare’ and Korn type inequalities, Forum Mathematicum 28 (3) 2008, 557–569.
  74. G. Alessandrini, E. Rosset, Symmetry of singular solutions of degenerate quasilinear elliptic equations, Rend. Istit. Mat. Univ. Trieste 39 (2007), 1-8.
  75. G. Alessandrini, V. Nesi, Beltrami operators, non-symmetric elliptic equations and quantitative Jacobian bounds,  Ann. Acad. Sci. Fenn. Math. 34, 2009, 47-67.
  76. G. Alessandrini, V. Nesi, Elliptic systems and material interpenetration, Funct. Approx. Comment. Math., 40 ( 1), 2009, 105-115, link to Arxiv.
  77. G. Alessandrini, E. Cabib, EIT and the average conductivity, J. Inv. Ill-Posed Problems 16, 8, 2008, 727–736, link to the preprint.
  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.
  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.
  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.
  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.

 

 

 

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.

 

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 s-harmonic mappings and applications, Newton Institute preprint NI00006-SMM.
  4. G. Alessandrini, L. Rondi, Corrigendum: Determining a sound-soft polyhedral scatterer by a single far-field measurement, link to Arxiv.