Inverse spectral problems for higher-order coefficients

Abstract: We establish uniqueness and stability inequalities for the problem of determining the higher-order coefficients of an elliptic operator from the corresponding boundary spectral data (BSD). Our analysis relies on the relationship between boundary spectral data and elliptic and hyperbolic Dirichlet to Neumann (DtN) maps. We also show how to adapt our analysis to obtain uniqueness and stability inequalities for determining the conductivity or the potential in an elliptic operator from the corresponding BSD.