Asymptotics for singular solutions to conformally invariant fourth order systems in the punctured ball.

We study asymptotic profiles for singular solutions to a class of critical strongly coupled fourth order systems on the punctured ball. Assuming a superharmonicity condition, we prove that sufficiently close to the isolated singularity, singular solutions behave like the so-called Emden–Fowler solution to the blow-up limit problem. On the technical level, we use an involved spectral analysis to study the Jacobi fields' growth properties in the kernel of the linearization of our system around a blow-up limit solution, which may be of independent interest. Our main theorem positively answers a question posed by Frank and König (2019) [12] concerning the local behavior of singular solutions close to the isolated singularity for scalar solutions in the punctured ball. It also extends to the case of strongly coupled systems, the celebrated asymptotic classification due to Korevaar et al. (1999) [21]. [ABSTRACT FROM AUTHOR]