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Inverse Problems and Imaging (IPI)
 

Stable determination of surface impedance on a rough obstacle by far field data

Pages: 341 - 351, Volume 7, Issue 2, May 2013      doi:10.3934/ipi.2013.7.341

 
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Giovanni Alessandrini - Dipartimento di Matematica e Geoscienze, Università degli Studi di Trieste, Via Valerio 12/1, 34127 Trieste, Italy (email)
Eva Sincich - Dipartimento di Matematica e Geoscienze, Università degli Studi di Trieste, Via Valerio 12/1, 34127 Trieste, Italy (email)
Sergio Vessella - Dipartimento di Matematica e Informatica "Ulisse Dini", Università degli Studi di Firenze, Viale Morgagni, 67/a - 50134 Firenze, Italy (email)

Abstract: We treat the stability of determining the boundary impedance of an obstacle by scattering data, with a single incident field. A previous result by Sincich (SIAM J. Math. Anal. 38, (2006), 434-451) showed a log stability when the boundary of the obstacle is assumed to be $C^{1,1}$-smooth. We prove that, when the obstacle boundary is merely Lipschitz, a log-log type stability still holds.

Keywords:  Inverse scattering problem, impedance boundary condition, stability.
Mathematics Subject Classification:  Primary: 35R30, 35R25; Secondary: 31B20.

Received: July 2012;      Revised: January 2013;      Available Online: May 2013.

 References