论文标题
LAMM-RIVIERE系统I：$ l^p $规律性理论
The Lamm-Riviere system I: $L^p$ regularity theory
论文作者
论文摘要
通过对Biharmonic映射的热流和气泡分析的动机，我们研究了第四阶Lamm-Riviere系统的进一步规律性问题$$Δ^{2} u =δ（v \ cdot \ nabla U）+{\ rm div}（\ nabla u）属于某些自然功能空间的不均匀术语$ f $。我们获得了弱解决方案的最佳高阶规则性和锋利的持有人连续性。在几种应用中，我们得出了具有均匀界限能量的弱溶液序列的弱紧凑性，这概括了近似Biharmonic映射的弱收敛理论。
Motived by the heat flow and bubble analysis of biharmonic mappings, we study further regularity issues of the fourth order Lamm-Riviere system $$Δ^{2}u=Δ(V\cdot\nabla u)+{\rm div}(w\nabla u)+(\nablaω+F)\cdot\nabla u+f$$ in dimension four, with an inhomogeneous term $f$ which belongs to some natural function space. We obtain optimal higher order regularity and sharp Holder continuity of weak solutions. Among several applications, we derive weak compactness for sequences of weak solutions with uniformly bounded energy, which generalizes the weak convergence theory of approximate biharmonic mappings.
