Borel–Pompeiu formula for a higher-order Lamé–Navier system in the plane

We establish a Borel–Pompeiu integral representation formula for a higher-order Lamé–Navier system of order p in the plane. Our approach is based on the construction of suitable fundamental kernels adapted to the higher-order structure. In particular, the classical Lamé–Navier system is recovered when p = 1, showing that the present results provide a natural higher-order extension of the complex-analytic approach to plane elasticity theory.