Local behavior and geometrical properties of
solutions to partial differential equations of elliptic and
parabolic type.
Inverse boundary value problems for elliptic
and parabolic equations and for elliptic systems.
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. TriesteXX, (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 Equations1996,
(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.58, 4, (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 Equations1998, (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 b328, (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:COCV7, (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 Problems18,
(2002), 1333-1353.
19. A. Morassi, E. Rosset, Detecting rigid inclusions, or
cavities, in an elastic body, Journal of Elasticity73, (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 Problems20,
(2004), 575-588.
22. A. Morassi, E. Rosset, Stable determination of caviries in
elastic bodies, Inverse Problems20, (2004),
453--480.
23. G. Alessandrini, A. Morassi, E. Rosset, Detecting an inclusion
in an elastic body by boundary measurements, SIAM Review46, (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 Problems21, (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 Problems25 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 (pdf).
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 (pdf).
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 (pdf).
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 265 (2018), 6400-6423 (pdf). 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., 231
(2019), 1455-1486 (pdf).
50. A. Morassi, E. Rosset, S. Vessella, Optimal stability in the
identification of a rigid inclusion in an isotropic
Kirchhoff-Love plate, SIAM J. Math. Anal., 51 (2019), 731-747 (pdf). 51. A. Bilotta, A.Morassi, E. Rosset, E. Turco, S.
Vessella, Numerical size estimates of inclusions in Kirchhoff-Love
elastic plates, International Journal of Solids and Structures,
168 (2019), 58-72 (pdf).
52. A. Morassi, E. Rosset, S. Vessella, Optimal identification of
a cavity in the Generalized Plane Stress problem in linear
elasticity, submitted.
53. A. Morassi, E. Rosset, S. Vessella, Doubling Inequality at the
Boundary for the Kirchhoff-Love Plate's Equation with Dirichlet
Conditions, Le Matematiche, LXXV (2020),
27-55, doi:
10.4418/2020.75.1.2, Open
access
.
54. A. Morassi, E. Rosset,
Estimating the area of extreme inclusions in Reissner-Mindlin
plates, Applicable
Analysis (2020), pubblicato online 27
marzo 2020, https://doi.org/10.1080/00036811.2020.1742885
(pdf).
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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