Stability for the multi-dimensional Borg-Levinson theorem with partial spectral data

Mourad Choulli (1) , Plamen Stefanov (2)

1 IECL - Institut Élie Cartan de Lorraine
2 Department of mathematics Purdue University

We prove a stability estimate related to the multi-dimensional Borg-Levinson theorem of determining a potential from spectral data: the Dirichlet eigenvalues k and the normal derivatives phi k / of the eigenfunctions on the boundary of a bounded domain. The estimate is of Holder type, and we allow finitely many eigenvalues and normal derivatives to be unknown. We also show that if the spectral data is known asymptotically only, up to O(k ) with >> 1, then we still have Holder stability.

Domaines: Equations aux dérivées partielles [math.AP]

Mourad Choulli, Plamen Stefanov. Stability for the multi-dimensional Borg-Levinson theorem with partial spectral data. Communications in Partial Differential Equations, 2013, 38 (3), pp.455-476. ⟨10.1080/03605302.2012.747538⟩. ⟨hal-01226906⟩