On the strong unique continuation of electromagnetic Schrödinger equations with random coefficients

Stochastic partial differential equations (SPDEs) with random coefficients are useful mathematical models for the quantification of perturbations in lots of complex engineering and physical applications. This paper mainly addresses the strong unique continuation property for the electromagnetic Schrödinger operator with random coefficients by the method proposed by N. Garofalo and F.H. Lin [10], [11]. Appropriate multipliers with physical backgrounds have been introduced to prove a priori estimates. Moreover, its application in an exact controllability problem has been shown, in which case, the boundary value determines the interior value completely.