Multidimensional Inverse Problems for Differential Equations

apply arbitrary arrive assume belong boundary conditions bounded chapter circle coefficients consider construct continuous function coordinates corresponding curves defined Denote derive determine determining a function differential equation direction domain earth's ellipses ellipsoid of revolution example exists expression family of curves fixed formula function u(r geometry given GREEN'S function half-plane half-space heat Hence holds inequality integral equation Introduce inverse problem inversion formula known linearized lying method moments multidimensional namely Notes obtain operator origin parameters plane polar problem for equation problem of determining properties proved question radius reduced relations represented respect right-hand side satisfies second kind similar solution to equation space spheres Substituting sufficient suppose surface telegraph equation tend theorem unique uniqueness theorem unit variables waves