On the determination of an inhomogeneity in an elliptic equation

Abstract

We consider the determination of the subdomain D, , in the boundary value problem (E_D ): −Δu + χ _Du = 0 in Ω and u = f on ∂Ω. To each admissible vector field V we associate the boundary measurements corresponding to the solution of , where D_V  = (I + V)D. This defines a mapping from the space of the admissible vector fields into the space of the boundary measurements. We show that this mapping is Gateaux-differentiable at V = 0 and its Gateaux derivative at this point is one to one.

Keywords:

• Elliptic equation
• Unknown subdomain

Keywords:

• AMS Subject Classification: 35R30