Multidimensional Inverse Problems for Differential Equations

absolutely integrable functions analytic function belong boundary conditions CAUCHY data chapter consider const construct continuous function corresponding cosk Denote derive determining a function differential equation domain earth's ellipses ellipsoid of revolution exists expression family of curves following theorem function u(r fundamental solution given GREEN'S function half-plane half-space HOLDER condition hyperplane inequality initial and boundary integral equation integral geometry integral-geometric problem Introduce the notation Inverse Kinematic Inverse Kinematic Problem inversion formula kernel L₁(D linearized inverse problem mean values multidimensional inverse problems obtain operator L defined parameters polar problem for equation problem of determining r₁ relations right-hand side second kind sense of HADAMARD solution to equation space STURM-LIOUVILLE equations take FOURIER transforms telegraph equation travel-times two-parameter family unique solution uniqueness theorem unit circle unknown function values over spheres variables velocity distribution VOLTERRA equation waves αφ