The Riemann-Hilbert problem with discontinuous coefficients for a Moisil-Theodoresco system with lower terms (Q1386204)

For the system \[ u_x+v_y +w_z+a_{11} s+a_{12} u+a_{13} v+a_{14} w=0,\;s_x-v_z+w_y +a_{21} s+a_{22} u+a_{23} v+a_{24} w=0, \] \[ s_y+u_z-w_x+ a_{31} s+a_{32} u+a_{33} v+a_{34} w=0,\;s_z-u_y+v_x +a_{41} s+a_{42} u+a_{43} v+a_{44} w=0, \] \[ a_{11} =-a_{44},\;a_{41} =a_{14}, \] consider the following problem: find a solution of this system regular in the domain \(D\subset\mathbb{R}^3\) subject to the conditions \[ s|_{z=0} =f_1(x,y),\;w|_{z= 0} =f_2(x,y), \quad u|_R =g_1 (\widetilde X),\;v|_R=f_2 (\widetilde X),\;\widetilde X\in \mathbb{R}. \]