Luca Rondi publications

My research activity deals with the study of partial differential equations, with the main focus on inverse problems associated to them. I am particularly interested in problems related to Electrical Impedance Tomography and Inverse Scattering. I am also interested in the Calculus of Variations, shape optimization and imaging.

Please find below a complete list of my publications. They are divided in articles in journals, theses and preprints. They are listed in chronological order of writing and not of printing. Whenever possible, they can be downloaded in pdf format. Otherwise, a link to the website of the journal in which the paper appeared is provided. In most cases the full text is available to subscribers. Preprints are available for download in pdf format. If you should have any problem in finding or downloading any of my papers, or if you would like any further information, please contact me (e-mail to rondi at units.it). Any comment, suggestion or remark will be greatly appreciated.

Articles in journals

  1. Giovanni Alessandrini and Luca Rondi, Stable determination of a crack in a planar inhomogeneous conductor, SIAM J. Math. Anal. 30 (2) (1998) 326-340.
  2. Luca Rondi, Uniqueness and stability for the determination of boundary defects by electrostatic measurements, Proc. Roy. Soc. Edinburgh Sect. A 130 (5) (2000) 1119-1151.
  3. Luca Rondi, Optimal stability estimates for the determination of defects by electrostatic measurements, Inverse Problems 15 (5) (1999) 1193-1212.
  4. Giovanni Alessandrini and Luca Rondi, Optimal stability for the inverse problem of multiple cavities, J. Differential Equations 176 (2) (2001) 356-386.
  5. Luca Rondi and Fadil Santosa, Enhanced Electrical Impedance Tomography via the Mumford-Shah Functional, ESAIM Control Optim. Calc. Var. 6 (2001) 517-538.
  6. Luca Rondi, Uniqueness for the determination of sound-soft defects in an inhomogeneous planar medium by acoustic boundary measurements, Trans. Amer. Math. Soc. 355 (1) (2003) 213-239.
  7. Michele Di Cristo and Luca Rondi, Examples of exponential instability for inverse inclusion and scattering problems, Inverse Problems 19 (3) (2003) 685-701.
  8. Luca Rondi, Unique determination of non-smooth sound-soft scatterers by finitely many far-field measurements, Indiana Univ. Math. J. 52 (6) (2003) 1631-1662.
  9. Giovanni Alessandrini, Laura Del Piero and Luca Rondi, Stable determination of corrosion by a single electrostatic boundary measurement, Inverse Problems 19 (4) (2003) 973-984.
  10. Giovanni Alessandrini and Luca Rondi, Determining a sound-soft polyhedral scatterer by a single far-field measurement, Proc. Amer. Math. Soc. 133 (6) (2005) 1685-1691.
    Corrigendum, preprint arXiv:math/0601406 (2006). Download (pdf file 70 Kb). Downloadable also from arXiv.org e-Print archive.
  11. Luca Rondi, Optimal stability of reconstruction of plane Lipschitz cracks, SIAM J. Math. Anal. 36 (4) (2005) 1282-1292.
  12. Michele Di Cristo, Luca Rondi and Sergio Vessella, Stability properties of an inverse parabolic problem with unknown boundaries, Ann. Mat. Pura Appl. (4) 185 (2) (2006) 223-255.
  13. Luca Rondi, A remark on a paper by Alessandrini and Vessella, Adv. in Appl. Math. 36 (1) (2006) 67-69.
  14. Luca Rondi, Unique continuation from Cauchy data in unknown non-smooth domains, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 5 (2) (2006) 189-218.
  15. Luca Rondi, A variational approach to the reconstruction of cracks by boundary measurements, J. Math. Pures Appl. (9) 87 (3) (2007) 324-342.
  16. Michele Di Cristo and Luca Rondi, Exponential instability for inverse elliptic problems with unknown boundaries, J. Phys.: Conf. Ser. 73 (Inverse Problems in Applied Sciences-towards breakthrough) (2007) 012005 (18 pp).
  17. Luca Rondi, Stable determination of sound-soft polyhedral scatterers by a single measurement, Indiana Univ. Math. J. 57 (3) (2008) 1377-1408.
  18. Luca Rondi, Reconstruction in the inverse crack problem by variational methods, European J. Appl. Math. 19 (6) (2008) 635-660.
  19. Luca Rondi, On the regularization of the inverse conductivity problem with discontinuous conductivities, Inverse Probl. Imaging 2 (3) (2008) 397-409.
  20. Giovanni Alessandrini, Luca Rondi, Edi Rosset and Sergio Vessella, The stability for the Cauchy problem for elliptic equations, Inverse Problems 25 (12) (2009) 123004 (47pp).

Theses

  1. Luca Rondi, Stabilità per il problema inverso dei crack in un corpo non omogeneo, degree thesis, Università degli Studi di Trieste, Trieste, 1996.
  2. Luca Rondi, Uniqueness and Optimal Stability for the Determination of Multiple Defects by Electrostatic Measurements, Ph.D. thesis, S.I.S.S.A.-I.S.A.S., Trieste, 1999.
    Download (pdf file 700 Kb). Downloadable also from S.I.S.S.A.-I.S.A.S. library's server.

Preprints

  1. Michele Di Cristo and Luca Rondi, Examples of exponential instability for elliptic inverse problems, preprint arXiv:math/0303126 (2003).
    Download (pdf file 460 Kb). Downloadable also from arXiv.org e-Print archive.
  2. Luca Rondi, Reconstruction of material losses by perimeter penalization and phase-field methods, preprint (2009).
    Download (pdf file 280 Kb). Downloadable also from arXiv.org e-Print archive.
  3. Lca Rondi and Fadil Santosa, Analysis of an Inverse Problem Arising in Photolithography, preprint (2010). new (22/2/2010)
    Download (pdf file 290 Kb). Downloadable also from arXiv.org e-Print archive.