SHARP MORREY REGULARITY THEORY FOR A FOURTH ORDER GEOMETRICAL EQUATION  

作　　者：向长林 郑高峰 Changlin XIANG;Gaofeng ZHENG(Three Gorges Mathematical Research Center,China Three Gorges University,Yichang,443002,China;School of Mathematics and Statistics,Central China Normal University,Wuhan,430079,China)

机构地区：[1]Three Gorges Mathematical Research Center,China Three Gorges University,Yichang,443002,China [2]School of Mathematics and Statistics,Central China Normal University,Wuhan,430079,China

出　　处：《Acta Mathematica Scientia》2024年第2期420-430,共11页数学物理学报（B辑英文版）

基　　金：supported by the National Natural Science Foundation of China(12271296,12271195).

摘　　要：This paper is a continuation of recent work by Guo-Xiang-Zheng[10].We deduce the sharp Morrey regularity theory for weak solutions to the fourth order nonhomogeneous Lamm-Rivière equation △^{2}u=△(V▽u)+div(w▽u)+(▽ω+F)·▽u+f in B^(4),under the smallest regularity assumptions of V,ω,ω,F,where f belongs to some Morrey spaces.This work was motivated by many geometrical problems such as the flow of biharmonic mappings.Our results deepens the Lp type regularity theory of[10],and generalizes the work of Du,Kang and Wang[4]on a second order problem to our fourth order problems.

关 键 词：fourth order elliptic equation regularity theory Morrey space decay estimates Riesz potential 

分 类 号：O175.25[理学—数学]