Integral equation of the 2-D problem of ajustment of stationary thermal fields

Ideas and methods of A.V. Tsirul'skii that have found application in gravity and magnetic inverse problems are adapted for the solution of stationary thermal problems in piecewise homogeneous media. For a simply connected region bounded by a regular analytical curve (K-parametrized, after Tsirul'skii), a closed solution to the boundary-value problem oftemperature ad ' justment in the forin of Cauchy integrals is derived. Piecewise analytical branches of Cauchy integrals on a Riemannian surface of symmetry solve the external and internal boundary-value problems of adjustment.