Unique recovery of a coefficient in an elliptic equation from input sources
Bruce D. Lowe, William Rundell · Inverse Problems · 1995
We consider the problem of determining the coefficient q(x) from the equation - Delta u j +qu j =f j on a bounded domain Omega contained in/implied by R n subject to Dirichlet boundary conditions. The non-homogeneous terms (f j ) 1 infinity form a complete set in L 2 ( Omega ). We prove that, under suitable conditions, a unique determination is possible from the net flux data. A numerical scheme to reconstruct the coefficient is suggested.