Overdetermined Systems of Linear Partial Differential Operators with Normal Principal Symbols

Elliptic complexes, made up of certain linear partial differential operators D1, …, Dd with C∞ coefficients, are constructed. The local solvability problem for the nonhomogeneous equations Dpu=f(p∈{1, …, d}) and the local integrability problem for the homogeneous equation D1u=0 are solved.