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apply arbitrary arrive assume belongs boundary conditions bounded chapter circle coefficient consider const 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 heat Hence holds inequality integral equation Introduce inverse problem known linearized method moments namely obtain operator origin parameters polar problem for equation problem of determining properties proved question radius reduced relations represented respect right-hand side satisfies similar ſº solution to equation space spheres Substituting sufficient suppose surface take FOURIER transforms telegraph equation theorem unique uniqueness theorem unit vanishes variables waves x,xn