Determining nonsmooth first order terms from partial boundary measurements

We extend results of Dos Santos Ferreira-Kenig-Sjöstrand-Uhlmann(arXiv:math.AP/0601466) to less smooth coefficients, and we show that measurements on part of the boundary for the magnetic Schrödinger operator determine uniquely the magnetic field related to a H¨older continuous potential. We give a similar result for determining a convection term. The proofs involve Carleman estimates, a smoothing procedure, and an extension of the Nakamura-Uhlmann pseudodifferential conjugation method to logarithmic Carleman weights.

Udgivelsesdato: MAY