The paper deals with a formulation of boundary conditions for numerical solving of partial derivative problems related to combined corona and electrostatic field analysis. Corona-electrostatic fields are frequently employed in multi-electrode systems to improve the performance of electrostatic processes or to give a new quality to them. Methods of analysis of such combined fields developed by other researches are overviewed. Method of complex potential functions is proposed by authors for analysis of electrostatic field in the multi-electrode system. Equation of field-line function with zero field strength value is used to compute the coordinates of points on the line separating areas with corona and electrostatic fields. Other outer boundary conditions of the field are determined from usual premises.