On the uniqueness of solution Cauchy's inverse problem for the equation Δu=au+b

Abstract

The inverse Cauchy problem

Δu(x)=au(x)+b≥0  for x∈ω,  and  u=0,   ∂u/∂ν=Φ   on γ

is shown as having a unique solution within a wide class of simply connected domains ω⋐R² with smooth boundary γ. Here a and b are real numbers to be determined, and Φ is a given function which is normalized by the condition ∫_γΦ ds=1.