The Lamm-Rivi\`ere system II: energy identity

TL;DR

This paper proves an angular energy quantization result for a fourth-order inhomogeneous Lamm-Rivi ext`ere system in four dimensions, extending understanding of energy concentration phenomena in such PDEs.

Contribution

It establishes an angular energy quantization for a complex fourth-order PDE system with inhomogeneous terms, advancing the analysis of energy distribution in these equations.

Findings

Proves angular energy quantization for the Lamm-Rivi ext`ere system

Handles inhomogeneous terms in the PDE

Extends previous energy quantization results to fourth-order systems

Abstract

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