On singular points of solutions of nonlinear higher-order elliptic equations and systems

A study is made of the behavior of solutions of nonlinear (as well as linear with discontinuous coefficients) elliptic equations and systems in a neighborhood of an isolated singular point. Under growth restrictions on the solution that depend on the index of the Cordes property of the system, it is established that the order of the singularity coincides with the order of the singularity of one of the singular solutions of the poly-Laplacian. Also considered are systems with a nonlinear potential, for which a complete classification of possible orders of the singularity is obtained, and conditions for the nonexistence of isolated singular points are determined.