On triviality of solutions for a generalised Giga-Kohn equation

Giga-Kohn equation is a particular semilinear elliptic equation of Ornstein-Uhlenbeck type that plays a central role in the description of singularities for the Fujita equation  - the semilinear heat equation with power law nonlinearity. In the 80' Giga and Kohn provided a key 'triviality theorem' concerning blow-up profiles in the Sobolev-subcritical regime that states, roughly speaking, that all singularities when viewed in a special coordinate system are locally flat. This result is derived from an extensive and fine-tuned Pohozaev-type calculation. A surprising aspect of the theory is that the argument is rigid and cannot be satisfyingly applied to simple generalisations of the Giga-Kohn equation. In my presentation I'll show some special cases where such extension was possible through a revision of the said Pohozaev-type calculation