Existence and Uniqueness Theorems in the Inverse Problem of Recovering Surface Fluxes from Pointwise Measurements

Inverse problems of recovering surface fluxes on the boundary a domain from pointwise observations are considered. Sharp conditions data ensuring existence and uniqueness solutions in Sobolev classes exposed. They smoothness data, geometric location measurement points, domain. The proof relies asymptotics fundamental to corresponding elliptic Laplace transform. inverse problem is reduced linear algebraic system with nondegerate matrix.