Inverse problems for real principal type operators
Recent developments in microlocal analysis October 14, 2019 - October 18, 2019
Location: MSRI: Simons Auditorium
Inverse boundary value problem
real principal type operator
propagation of singularities
We consider inverse boundary value problems for general real principal type differential operators. The first results state that the Cauchy data set uniquely determines the scattering relation of the operator and bicharacteristic ray transforms of lower order coefficients. We also give two different boundary determination methods for general operators, and prove global uniqueness results for determining coefficients in nonlinear real principal type equations. The article presents a unified approach for treating inverse boundary problems for transport and wave equations, and highlights the role of propagation of singularities in the solution of related inverse problems. This is joint work with Lauri Oksanen (UCL), Plamen Stefanov (Purdue) and Gunther Uhlmann (Washington / IAS HKUST).
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