The Lamm-Rivière system II: energy identity

Abstract

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

23 pages