首页|SHARP MORREY REGULARITY THEORY FOR A FOURTH ORDER GEOMETRICAL EQUATION
SHARP MORREY REGULARITY THEORY FOR A FOURTH ORDER GEOMETRICAL EQUATION
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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△2u=△(V▽u)+div(w▽u)+(▽ω+F)·▽u+f in B4,under the smallest regularity assumptions of V,(w),ω,F,where f belongs to some Morrey spaces.This work was motivated by many geometrical problems such as the flow of bihar-monic 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.
fourth order elliptic equationregularity theoryMorrey spacedecay estimatesRiesz potential
向长林、郑高峰
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Three Gorges Mathematical Research Center,China Three Gorges University,Yichang 443002,China
School of Mathematics and Statistics,Central China Normal University,Wuhan 430079,China
National Natural Science Foundation of ChinaNational Natural Science Foundation of China
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