Edi Rosset

Position: associate professor of Mathematical Analysis

Address:
Dipartimento di  Matematica e Geoscienze
Università degli Studi di Trieste
Via Valerio 12/1
34127 Trieste
Italy
tel. (+39) 040 558 2631
e-mail: rossedi@units.it
 
 

Research fields:

List of papers:

1. G. Mancini, E. Rosset, Alcune osservazioni su problemi  ellittici semilineari a simmetria radiale, Rend. Ist. Mat. Univ. TriesteXX, (1988), 307-318.
2. E. Rosset, Topological degree in  Rn, Rend. Ist. Mat. Univ. Trieste XX, (1988), 319-329.
3. E. Rosset, An analytic construction of the winding number of W1,n-1 maps from Sn-1 to n-manifolds with boundary,  Boll. Un. Mat. Ital. 5-B, (1991), 493-506.
4. E. Rosset, An existence result for minimal spheres in manifolds with boundary, Rend. Mat. Acc.Lincei1, (1990), 11-15.
5. E. Rosset, Singolarita' e comportamenti singolari in problemi ellittici semilineari, tesi di Dottorato di Ricerca, 1989.
6. G. Alessandrini, D. Lupo, E. Rosset, Local behavior and geometric properties of solutions to degenerate quasilinear elliptic equations in the plane, Appl. Anal. 50, (1993), 191-216.
7. E. Rosset, Isolated singularities of solutions to the equation div(a(|Du|)Du)=0 in the plane, Complex Variables 25, (1994), 69-96.
8. E. Rosset, An approximate Gidas-Ni-Nirenberg theorem, Math. Meth. Appl. Sci. 17, (1994), 1045-1052.
9. E. Rosset, A lower bound for the gradient of $\infty$-harmonic functions, Electron. J. Differential Equations 1996, (1996), No.  2, 1-7.
10. G. Alessandrini, E. Rosset, The inverse conductivity problem with one measurement: bounds on the size of the unknown object, SIAM J. Appl. Math. 584, (1998), 1060-1071.
11. 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.
12. E. Rosset, Symmetry and convexity of level sets of solutions to $\Delta_\infty u+f(u)=0$, Electron. J. Differential Equations 1998, (1998),  No. 34, 1-12.
13.  G. Alessandrini, E. Beretta, E. Rosset, S. Vessella, Optimal stability for inverse elliptic boundary value problems with unknown boundaries, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) XXIX, (2000), 755-806.
14 G. Alessandrini, E. Beretta, E. Rosset, S. Vessella, Inverse boundary value
problems with unknown boundaries: optimal stability, C. R. Acad.Sci. Paris S\'er. II b 328, (2000), 607-611.
15. B. Canuto, E. Rosset, S. Vessella, Quantitative estimates of unique continuation for parabolic equations and inverse initial-boundary value problems with unknown boundaries, Transactions Amer. Math. Soc., 354, (2002), 491-535.
16. B. Canuto, E. Rosset, S. Vessella, A stability result in the  localization of cavities in a thermic conducting medium,  ESAIM:COCV  7, (2002), 521-565.
17. G. Alessandrini, A. Morassi, E. Rosset, Detecting an inclusion in an elastic body by boundary measurements, SIAM J. Math. Anal. 33, (2002), 1247-1268.
18. G. Alessandrini, A. Morassi, E. Rosset, Detecting cavities by electrostatic boundary measurements, Inverse Problems 18, (2002), 1333-1353. 
19.  A. Morassi, E. Rosset, Detecting rigid inclusions, or cavities, in an elastic body, Journal of Elasticity 73, (2003), 101--126.
20. G. Alessandrini, A. Morassi, E. Rosset, Size estimates, Contemporary Mathematics, 333, (2003), 1-33.
21. G. Alessandrini, E. Rosset, Volume bounds of inclusions from physical EIT measurements,  Inverse Problems 20, (2004), 575-588.
22. A. Morassi, E. Rosset, Stable determination of caviries in elastic bodies, Inverse Problems 20, (2004), 453--480.
23. G. Alessandrini, A. Morassi, E. Rosset, Detecting an inclusion in an elastic body by boundary measurements, SIAM Review  46, (2004), 477-498 (revised and updated version of [17]) .
24. G. Alessandrini, A. Bilotta, G. Formica, A. Morassi, E. Rosset, E. Turco, Numerical size estimates of inclusions in elastic bodies,  Inverse Problems 21, (2005), 133-151.
25. A. Morassi, E. Rosset, Uniqueness and stability in determining a rigid inclusion in an elastic body, Mem. Amer. Math. Soc. 200 (938), (2009).
26. 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, (2007), 288-306.
27. A. Morassi, E. Rosset, S. Vessella, Size estimates for inclusions in an elastic plate by boundary measurements, Indiana Univ. Math. J., 56, (2007), 2325-2384.
28. G. Alessandrini, A. Morassi, E. Rosset, The linear constraints in Poincarè and Korn type inequalities, Forum Math., 20, (2008), 557-569.
29. A. Morassi, E. Rosset, S. Vessella, Unique determination of a cavity in an elastic plate by two boundary measurements, Inverse Prob. Imaging, 1, (2007), 481-506.
30. G.Alessandrini, A. Bilotta, G. Formica, A. Morassi, E. Rosset, E. Turco, Computing volume bounds of inclusions by EIT measurements, J. Sci. Comp. 33, (2007), 293-312.
31. G. Alessandrini, E. Rosset, Symmetry of singular solutions of degenerate quasilinear elliptic equations, Rend. Istit. Mat. Univ.Trieste 39 (2007), 1-8.
32. E. Rosset, Problem solving e gara di matematica a squadre ``Coppa Aurea'', in ``Con le mani e con la mente. I laboratori di matematica del Progetto Lauree Scientifiche dell'Università di Trieste'' (2008), EUT, Trieste, 120-128.
33. G. Alessandrini, A. Morassi, E. Rosset, S. Vessella, On doubling inequalities for elliptic systems, J. Math. Anal. Appl. 357 (2), (2009), 349-355.
34. A. Morassi, E. Rosset, S. Vessella, Detecting general inclusions in elastic plates, Inverse Problems 25 045009, (2009) , 1-14 (abstract).
35. A. Morassi, E. Rosset, Unique determination of unknown boundaries in an elastic plate by one measurement, Comptes Rendus Mécanique,  338 (2010), 450-460.
36. G.Alessandrini, L. Rondi, E. Rosset, S. Vessella, The stability for the Cauchy problem for elliptic equations, Inverse Problems 25 123004, (2009), 1-47.
37. A. Morassi, E. Rosset, 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, Journal of Functional Analysis 261, (2011), 1494-1541.
38. A. Morassi, E. Rosset, S. Vessella, Stable determination of a rigid inclusion in an anisotropic elastic plate, SIAM J. Math. Anal.44, (3) (2012), 2204-2235.
39. A. Morassi, E. Rosset, S. Vessella, Estimating area of inclusions in anisotropic plates from boundary data,  Discrete Contin. Dyn. Syst. Ser. S 6 (2013), 501-515.
40. A. Morassi, E. Rosset, S. Vessella, Recent results about the detection of unknown boundaries and inclusions in elastic plates, J. Inverse Ill-Posed Probl. 21 (2013), 311-352.
41. M. Di Cristo, C.-L. Lin, A. Morassi, E. Rosset, S. Vessella, J.-N. Wang, Doubling inequalities for anisotropic plate equations and applications to size estimates of inclusions, Inverse Problems, 29 (2013), 1-17.
42. 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 (2014), 2692-2729.
43. E. Beretta, E. Francini, A. Morassi, E. Rosset, S. Vessella, Lipschitz continuous dependence of piecewise constant Lamè coefficients from boundary data: the case of non flat interfaces, Inverse Problems, 30 (2014) 125005, 1-18 (abstract).

44. G. Alessandrini, A. Morassi, E. Rosset, S. Vessella, Global stability for an inverse problem in soil-structure interaction, Proc. R. Soc. A 471 (2015), 20150117.
45.
A. Morassi, E. Rosset, Stable determination of an inclusion in an inhomogeneous elastic body by boundary measurements, Rend. Istit. Mat. Univ. Trieste, Volume 48 (2016), 101-120.
46. A. Morassi, E. Rosset, S. Vessella, A generalized Korn inequality and strong unique continuation for the Reissner–Mindlin plate system, J. Differential Equations 263 (2017), 811–840.
47. A. Morassi, E. Rosset, S. Vessella, Size estimates for fat inclusions in an isotropic Reissner-Mindlin plate, Inverse Problems, 34 (2018), 025001, 1-26.
48. A. Aspri, E. Beretta, E. Rosset, On an elastic model arising from volcanology: an analysis of the direct and inverse problem, J. Differential Equations, to appear.
49. 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., to appear.
Conference Proceedings

1.  G. Alessandrini, E. Rosset, Efficient detection of an inclusion in a conductor, Proceedings IMACS Symposium on Mathematical Modelling (1997), Vienna, 1015--1020.
2. A. Morassi, E. Rosset, Stable determination of unknown boundaries in elastic bodies, International Conference "Inverse Problems: Modeling and Simulation", H.T. Banks, A. Hasanov and S.I. Kabanikhin Editors, Fethiye (Turkey), 120-122, June 7-12, 2004.
3. A. Morassi, E. Rosset, Detection  of a rigid inclusion in an elastic body: uniqueness and stability, in "Systems, Control, Modeling and Optimization",  F. Ceragioli, A. Dontchev, H. Furuta, K. Marti, L. Pandolfi Editors,  Proceedings of the 22nd IFIP TC7 Conference, Torino, 279--284, July 18-22, 2005.

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