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Based on the three-ball inequality and the doubling inequality established in[24], we quantify the strong unique continuation for an elliptic operator withunbounded lower order coefficients. This result is then used to improve thequantitative unique continuation from a set of positive measure obtained in[24]. We also derive a uniform quantitative strong unique continuation foreigenfunctions that we use to prove that two Dirichlet-Laplace-Beltramioperators are gauge equivalent whenever their corresponding metrics coincide inthe vicinity of the boundary and their boundary spectral data coincide on asubset of positive measure.

Quantitative strong unique continuation for elliptic operators -- application to an inverse spectral problem