Conditional stability for an inverse source problem and an application to the estimation of air dose rate of radioactive substances by drone data

We consider the density field f(x) generated by a volume source μ(y) in D which is a domain in R3. For two disjoint segments γ, Γ1 on a straight line in R3 \ D , we establish a conditional stability estimate of Hölder type in determining f on Γ1 by data f on γ. This is a theoretical background for real-use solutions for the determination of air dose rates of radioactive substance at the human height level by high-altitude data. The proof of the stability estimate is based on the harmonic extension and the stability for line unique continuation of a harmonic function.