Statistical approach to inverse boundary problems for partial differential equations
- Golubev, Georgi
- Khasminskii, Rafail
2010 Mathematics Subject Classification
- Partial differential equation, minimax estimator, boundary problem
Inverse problems for elliptic and parabolic partial differential equations are considered. It is assumed that a solution of the equation is observed in white Gaussian noise with a small spectral density. The goal is to recover smooth but unknown boundary or initial conditions based on the noisy data. It is shown that the second order minimax estimators are linear as the spectral density of the noise goes to zero.