Elisa Francini Research

Università degli Studi di Firenze Dipartimento di Matematica e Informatica "Ulisse Dini" Viale Morgagni 67A, 50134 Firenze Tel: +39 055 2751406 E-mail: elisa.francini"at"unifi.it

Preprints

E. Francini, S. Vessella, J.N. Wang, Propagation of smallness and size estimate in the second order elliptic equation with discontinuous complex Lipschitz conductivity Arxiv version

E. Francini, S. Vessella, J.N. Wang, Carleman estimate for complex second order elliptic operators with discontinuous Lipschitz coefficients Arxiv version

Publications

[40] Beretta E., Francini E. (In corso di stampa). Global Lipschitz stability estimates for polygonal conductivity inclusions from boundary measurements. APPLICABLE ANALYSIS. Link to Arxiv version

[39] Shi J.; Beretta E.; de Hoop M.V.; Francini E.; Vessella S. (2020). A numerical study of multi-parameter full waveform inversion with iterative regularization using multi-frequency vibroseis data. COMPUTATIONAL GEOSCIENCES, vol. 24, pp. 89-107.

[38] Francini E., Franzina G., Vessella S. (2020). Existence and regularity for eddy current system with non-smooth conductivity, SIAM JOURNAL ON MATHEMATICAL ANALYSIS, vol. 52, pp. 2134-2157. Link to Arxiv version

[37] Beretta, E., Francini E., Vessella S. (2019), A transmission problem on a polygonal partition: regularity and shape differentiability, Applicable Analysis, vol. 98, pp. 1862-1874. Link to Arxiv version

[36] Francini, E., Vessella, S., Carleman estimates for the parabolic transmission problem and Hoelder propagation of smallness across an interface, JOURNAL OF DIFFERENTIAL EQUATIONS, 265 (2018) 2375-2430. Link to Arxiv version

[35] Beretta, E., Francini, E., Vessella, S. Differentiability of the Dirichlet to Neumann map under movements of polygonal inclusions with an application to shape optimization, SIAM JOURNAL ON MATHEMATICAL ANALYSIS, vol. 49, pp. 756-776 (2017) Link to Arxiv

[34] Di Fazio, G., Francini, E., Raciti, F., Vessella, S., Stable determination of a Lamé coefficient by one internal measurement of displacement, JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, vol. 452, pp. 388-400 (2017) Link to Arxiv

[33] M. Di Cristo, E. Francini, C.-L. Lin, S. Vessella, J.-N. Wang, Carleman estimate for second order elliptic equations with Lipschitz leading coefficients and jumps at an interface, Journal de Mathematiques Pures et Appliquee, vol. 108, pp. 163-206 (2017) Link to Arxiv

[32] G. Alessandrini, M. Di Cristo, E. Francini, S. Vessella, Stability for quantitative photoacoustic tomography with well chosen illuminations, Annali di Matematica Pura e Applicata, 196, n.2 (2017) 395-406. Link to Arxiv

[31] E. Beretta, M.V. de Hoop, E. Francini, S. Vessella, J. Zhai, Uniqueness and Lipschitz stability of an inverse boundary value problem for time-harmonic elastic waves, INVERSE PROBLEMS, vol. 33, n. 3, 035013 (2017) Link to Arxiv

[30] E. Francini, C.-L. Lin, S. Vessella, J.-N. Wang, Three-region inequalities for the second order elliptic equation with discontinuous coefficients and size estimate, JOURNAL OF DIFFERENTIAL EQUATIONS, vol. 261, pp. 5306-5323 (2016), Link to Arxiv

[29] E. Beretta, E. Francini, Asymptotic formulas for steady state voltage potentials in the presence of thin inhomogeneities. The complex case, Rend. Istit. Mat. Univ. Trieste, vol. 48, pp. 209-219 (2016).

[28] E. Beretta, M.V. de Hoop, E. Francini, S. Vessella, Stable determination of polyhedral interfaces from boundary data for the Helmholtz equation., Comm. PDE 40, no. 7, (2015), 1365�1392. MR3341208 arxiv

[27] E. Beretta, E. Francini, A. Morassi, E. Rosset, S. Vessella, Lipschitz continuous dependence of piecewise constant Lam� coefficients from boundary data: the case of non flat interfaces., Inverse Problems, 30, no. 12 (2014), 125005, 18 pp. MR3291119 Link to Arxiv

[26] E. Beretta, E. Francini, S. Vessella, Uniqueness and Lipschitz stability for the identification of Lam� parameters from boundary measurements, Inverse Problems and Imaging, 8 (2014), 611-644. MR3295939 Link to Arxiv

[25] E. Beretta, E. Francini, S. Vessella, Size estimates for the EIT problem with one measurement: The complex case, Revista Matematica Iberoamericana, 30 (2014), 551-580. MR3231210 Link to Arxiv

[24] E. Beretta, E. Bonnetier, E. Francini, A.L. Mazzucato, Small volume asymptotics for anisotropic elastic inclusions, Inverse Problems and Imaging, 6 (2012) 1-23. MR2887190 Link to Arxiv

[23] E. Beretta, E. Francini Lipschitz stability for the electrical impedance tomography problem: the complex case , Communications in PDE, 36 (2011), 1723-1749. MR2832161 Link to Arxiv

[22] E. Beretta, E. Francini, E. Kim, J. Lee, Algorithm for the determination of a linear crack in an elastic body from boundary measurements, Inverse Problems 26 (2010) 085015 (13pp). MR2661694

[21] H. Ammari, E. Beretta, E. Francini, H. Kang, M. Lim, Reconstruction of small interface changes of an inclusion from modal measurements II: The elastic case. Journal de Math�matiques Pures et Appliqu�es 94 n.3 (2010), 322-339. MR2679030

[20] E. Beretta, Y. Capdeboscq, F. De Gournay, E. Francini, Thin cylindrical conductivity inclusions in a three-dimensional domain: polarization tensor and unique determination from boundary data, Inverse Problems 25 n.6 (2009) 065004 22pp MR2506849

[19] H. Ammari, E. Beretta, E. Francini, H. Kang, M. Lim, Optimization algorithm for reconstructing interface changes of a conductivity inclusion from modal measurements, Mathematics of Computation, 79 (2010), 1757-1777 . MR2630011

[18] E. Beretta, E. Francini, S. Vessella, Determination of a linear crack in an elastic body from boundary measurements - Lipschitz Stability, SIAM Journal of Mathematical Analysis, 40 (2008), 984--1002. MR2443262

[17] E. Beretta, E. Francini, An asymptotic formula for the displacement field in the presence of thin elastic inhomogeneities, SIAM Journal of Mathematical Analysis, 38 (2006), 1249--1261. MR2274482

[16] T. Hoft, E. Francini, F. Santosa, An inverse problem in nondestructive evaluation of spot-welds, Inverse Problems, 22 (2006) 645-661. MR2216420

[15] H. Ammari, E. Beretta, E. Francini, Reconstruction of thin conductivity imperfections, II. The case of multiple segments, Applicable Analysis, Vol. 85, No.1-3, (2006), 87-105.MR2198833

[14] H. Ammari, E. Beretta, E. Francini, Reconstruction of thin conductivity imperfections , Applicable Analysis, Vol. 83, No.1, (2004), 63-76. MR2031608

[13] E. Beretta, E. Francini, Asymptotic formulas for perturbations in the electromagnetic fields due to the presence of thin inhomogeneities. Contemporary Mathematics, vol. 333 (2003), 49-62. MR2032006

[12] E. Beretta, E. Francini, M. Vogelius Asymptotic formulas for steady state voltage potentials in the presence of thin inhomogeneities. A rigorous error analysis , Journal de Mathematiques Pures et Appliquee, Vol. 82, 10, (2003), 1277-1301.MR2020923

[11] E. Francini, Recovering a complex coefficient in a planar domain from the Dirichlet-to-Neumann map Inverse Problems, 16 (2000), 107-119. MR1741230

[10] A. Colesanti, E. Francini, P. Salani, Convexity and asymptotic estimates for large solutions of Hessian equations, Differential and Integral Equations, 13, (2000), 1459-1472.MR1787077PDF

[9] E. Francini, Stability results for a linear parabolic noncharacteristic Cauchy problem, Journal of Ill-Posed and Inverse Problems, 8, n.3, (2000), 255-272. MR1781351

[8] V.L.Kamynin, E.Francini, Asymptotic behavior of solutions of some inverse problems for higher order parabolic equations , Russian Journal of Mathematical Physics, 6, n.4, (1999), 394-408. MR1815360

[7] F. De Vita, E. Francini, Commenti sui dati statistici universitari nell'ultimo trentennio, La matematica nella cultura e nella società, Boll. Unione Mat. Ital., (8) 1-A (1998), 111-120.

[6] E. Francini, A. Greco, Blow-up in exterior domains: existence and star-shapedness, Zeitschrift fur Analysis und ihre Anwendungen, 17, (1998) n.2, 431-441. MR1632571

[5] V.L.Kamynin, M.Saroldi, E.Francini, Inverse Problems for Higher Order Parabolic Equations, (Joint sessions of the Petrovskii Seminar and the Moscow Mathematical Society, 1998) Russian Mathematical Surveys, 53, n.4, (1998), 202-203.

[4] V. Kamynin, E. Francini, An inverse problem for higher order parabolic equation, Mathematical Notes, 64, n.5, (1998), 590-599. MR1691210

[3] E. Francini, Starshapedness of level sets for solutions of nonlinear elliptic equations, Math. Nachr. 193 (1998), 49-56. MR1637578

[2] E. Francini, Starshapedness of level sets for solutions of nonlinear parabolic equations, Rendiconti dell'Istituto di Matematica dell'Università di Trieste, 28 (1996), 49-62.MR1463908

[1] E. Francini, Sul principio di massimo per l'angolo formato dal gradiente di soluzioni di equazioni ellittiche con una direzione fissata, Boll. Unione Mat. Ital., (7) 9-A (1995), 123-130. MR1324612