### 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articles appeared in journals or submitted, theses and unpublished
preprints.
They are listed in
chronological order of writing and not of printing.
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
`luca.rondi at unimi.it`).
Any comment, suggestion or remark will be greatly appreciated.

### Articles in journals

- Giovanni Alessandrini and Luca Rondi,
*Stable determination of a crack in a planar inhomogeneous conductor*, SIAM J. Math. Anal.**30**(2) (1998) 326-340. - 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. - Luca Rondi,
*Optimal stability estimates for the determination of defects by electrostatic measurements*, Inverse Problems**15**(5) (1999) 1193-1212. - Giovanni Alessandrini and Luca Rondi,
*Optimal stability for the inverse problem of multiple cavities*, J. Differential Equations**176**(2) (2001) 356-386. - Luca Rondi and Fadil Santosa,
*Enhanced Electrical Impedance Tomography*via*the Mumford-Shah Functional*, ESAIM Control Optim. Calc. Var.**6**(2001) 517-538. - 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. - Michele Di Cristo and Luca Rondi,
*Examples of exponential instability for inverse inclusion and scattering problems*, Inverse Problems**19**(3) (2003) 685-701. - 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. - 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. - 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) - Luca Rondi,
*Optimal stability of reconstruction of plane Lipschitz cracks*, SIAM J. Math. Anal.**36**(4) (2005) 1282-1292. - 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. - Luca Rondi,
*A remark on a paper by Alessandrini and Vessella*, Adv. in Appl. Math.**36**(1) (2006) 67-69. - 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. - Luca Rondi,
*A variational approach to the reconstruction of cracks by boundary measurements*, J. Math. Pures Appl. (9)**87**(3) (2007) 324-342. - 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). - Luca Rondi,
*Stable determination of sound-soft polyhedral scatterers by a single measurement*, Indiana Univ. Math. J.**57**(3) (2008) 1377-1408. - Luca Rondi,
*Reconstruction in the inverse crack problem by variational methods*, European J. Appl. Math.**19**(6) (2008) 635-660. - Luca Rondi,
*On the regularization of the inverse conductivity problem with discontinuous conductivities*, Inverse Probl. Imaging**2**(3) (2008) 397-409. - 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). - Luca Rondi,
*Reconstruction of material losses by perimeter penalization and phase-field methods*, J. Differential Equations**251**(1) (2011) 150-175. - Luca Rondi and Fadil Santosa,
*Analysis of an Inverse Problem Arising in Photolithography*, Math. Models Methods Appl. Sci.**22**(5) (2012) 1150026 (30pp). - Wolfgang Ring and Luca Rondi,
*Reconstruction of cracks and material losses by perimeter-like penalizations and phase-field methods*:*numerical results*, Interfaces Free Bound.**13**(3) (2011) 353-371. - Giorgio Menegatti and Luca Rondi,
*Stability for the acoustic scattering problem for sound-hard scatterers*, Inverse Probl. Imaging**7**(4) (2013) 1307-1329. -
Jingzhi Li, Hongyu Liu, Luca Rondi and Gunther Uhlmann,
*Regularized Transformation-Optics Cloaking for the Helmholtz Equation*:*From Partial Cloak to Full Cloak*, Comm. Math. Phys.**335**(2) (2015) 671-712. -
Luca Rondi and Mourad Sini,
*Stable determination of a scattered wave from its far-field pattern*:*the high frequency asymptotics*, Arch. Ration. Mech. Anal.**218**(1) (2015) 1-54. -
Luca Rondi,
*Continuity properties of Neumann-to-Dirichlet maps with respect to the H-convergence of the coefficient matrices*, Inverse Problems**31**(4) (2015) 045002 (24pp). -
Luca Rondi, Fadil Santosa and Zhu Wang,
*A variational approach to the inverse photolithography problem*, SIAM J. Appl. Math.**76**(1) (2016) 110-137. -
Hongyu Liu, Michele Petrini, Luca Rondi and Jingni Xiao,
*Stable determination of sound-hard polyhedral scatterers by a minimal number of scattering measurements*, J. Differential Equations**262**(3) (2017) 1631-1670. -
Luca Rondi,
*A Friedrichs-Maz'ya inequality for functions of bounded variation*, Math. Nachr.**290**(11-12) (2017) 1830-1839. -
Luca Rondi,
*Discrete approximation and regularisation for the inverse conductivity problem*, Rend. Istit. Mat. Univ. Trieste**48**(2016) 315-352. -
Hongyu Liu, Luca Rondi and Jingni Xiao,
*Mosco convergence for H*(curl)*spaces, higher integrability for Maxwell's equations, and stability in direct and inverse EM scattering problems*, J. Eur. Math. Soc. (JEMS)**21**(10) (2019) 2945-2993. -
Maria Giovanna Mora, Luca Rondi and Lucia Scardia,
*The equilibrium measure for a nonlocal dislocation energy*, Comm. Pure Appl. Math.**72**(1) (2019) 136-158. -
José Antonio Carrillo, Joan Mateu, Maria Giovanna Mora, Luca Rondi,
Lucia Scardia and Joan Verdera,
*The ellipse law: Kirchhoff meets dislocations*, Comm. Math. Phys.**373**(2) (2020) 507-524. -
Klas Modin, Adrian Nachman and Luca Rondi,
*A Multiscale Theory for Image Registration and Nonlinear Inverse Problems*, Adv. Math.**346**(2019) 1009-1066. -
Michele Di Cristo and Luca Rondi,
*The distance from the boundary in a Riemannian manifold*:*regularity up to a conformal change of the metric*, Indiana Univ. Math. J., to appear.

Download a preprint version. -
Michele Di Cristo and Luca Rondi,
*Interior decay of solutions to elliptic equations with respect to frequencies at the boundary*, Indiana Univ. Math. J., to appear.

Download a preprint version. -
José Antonio Carrillo, Joan Mateu, Maria Giovanna Mora, Luca Rondi,
Lucia Scardia and Joan Verdera,
*The equilibrium measure for an anisotropic nonlocal energy*, Calc. Var. Partial Differential Equations, to appear.

Download a preprint version. -
Joan Mateu, Maria Giovanna Mora, Luca Rondi,
Lucia Scardia and Joan Verdera,
*A maximum-principle approach to the minimisation of a nonlocal dislocation energy*, Mathematics in Engineering**2**(2) (Special issue*Variational Models in Elasticity*) (2020) 253-263. -
Joan Mateu, Maria Giovanna Mora, Luca Rondi,
Lucia Scardia and Joan Verdera,
*Explicit minimisers of some nonlocal anisotropic energies*:*a short proof*, Izv. Math., to appear.

Download a preprint version. -
Luca Rondi, Eva Sincich and Mourad Sini,
*Stable determination of a rigid scatterer in elastodynamics*, SIAM J. Math. Anal.**53**(2) (2021) 2660-2689.

### Theses

- Luca Rondi,
*Stabilità per il problema inverso dei crack in un corpo non omogeneo*, degree thesis, Università degli Studi di Trieste, Trieste, 1996. - 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.

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### Preprints

- Michele Di Cristo and Luca Rondi,
*Examples of exponential instability for elliptic inverse problems*, preprint arXiv:math/0303126, 2003.

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