The Holmgren’s problem analogue of the four-dimensional degenerate elliptic equation

The solvability issues of the Holmgren’s problem analogue of the four-dimensional degenerate second order elliptic equation are studied in the finite domain, where values of the function are set in one part of the boundary and normal derivatives are set in another piecewise smooth part of the boundary. Using the corresponding fundamental solution of the problem for the four-dimensional generalized Gellerstedt equation obtained earlier in the paper of Berdyshev, Hasanov and Ryskan (Fundamental solutions for a class of four-dimensional degenerate elliptic equation, Complex Var. Elliptic Equ. 65(4), 632-647 (2020)) we constructed Green’s function. We use various properties of the hypergeometric Laurichella’s functions to study the problem solvability issues.