The Lamm-Rivière system II: energy identity

In this paper, we establish an angular energy quantization for the following fourth order inhomogeneous Lamm-Rivière system $${\mathrm{\Delta }}^{2}u=\mathrm{\Delta }(V\cdot \mathrm{\nabla }u)+\text{div}(w\mathrm{\nabla }u)+W\cdot \mathrm{\nabla }u+f$$ in dimension four, with an inhomogeneous term $f\in L\log L$.