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▽...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.展开更多
Let M be a C^(2)-smooth Riemannian manifold with boundary and X be a metric space with non-positive curvature in the sense of Alexandrov.Let u:M→X be a Sobolev mapping in the sense of Korevaar and Schoen.In this shor...Let M be a C^(2)-smooth Riemannian manifold with boundary and X be a metric space with non-positive curvature in the sense of Alexandrov.Let u:M→X be a Sobolev mapping in the sense of Korevaar and Schoen.In this short note,we introduce a notion of p-energy for u which is slightly different from the original definition of Korevaar and Schoen.We show that each minimizing p-harmonic mapping(p≥2)associated to our notion of p-energy is locally Holder continuous whenever its image lies in a compact subset of X.展开更多
蜘蛛作为草原生态系统中的主要消费者,对维系草原生物多样性和生态系统功能具有重大意义。放牧是人类利用草原最普遍的方式,了解放牧对蜘蛛多样性的影响具有重要生态学意义。本研究调查了内蒙古赛罕乌拉草原上5个不同放牧强度样地中的...蜘蛛作为草原生态系统中的主要消费者,对维系草原生物多样性和生态系统功能具有重大意义。放牧是人类利用草原最普遍的方式,了解放牧对蜘蛛多样性的影响具有重要生态学意义。本研究调查了内蒙古赛罕乌拉草原上5个不同放牧强度样地中的蜘蛛多样性,通过单因素方差分析(one-wayanalysisofvariance)比较各样地中的蜘蛛多样性,非度量多维标度分析(non-metric multidimensional scale,NMDS)和相似性分析(analysis of similarities,ANOSIM)比较各样地间的蜘蛛物种组成相似性,再结合相关性分析探讨了植被高度对蜘蛛多样性的影响。结果表明:重度放牧强度样地的蜘蛛多样性显著低于其他未放牧及轻度放牧样地;具体到常见科上,放牧强度对织网型的园蛛物种数和个体数影响显著,而对游猎型的狼蛛、跳蛛却不明显;织网型蜘蛛主要受植被结构影响,而游猎型蜘蛛更可能受潜在猎物可得性的影响。NMDS分析表明不同放牧强度下,蜘蛛类群的物种组成呈现明显的梯度变化,放牧强度越低,物种组成和未放牧样地越相近。相关性分析表明草原植被高度与蜘蛛多样性总体上呈正相关关系,即植被高度越高,蜘蛛多样性越高。其中依靠植物构建蛛网的园蛛科和在植物上层伏击猎物的蟹蛛科、逍遥蛛科等与植被高度显著相关。这说明植物资源及其空间异质性可能对草原蜘蛛多样性起着主导作用。因此,降低放牧强度有助于保护草原蜘蛛群落的多样性,特别有利于织网型蜘蛛。展开更多
基金supported by the National Natural Science Foundation of China(12271296,12271195).
文摘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.
基金supported by the Qilu funding of Shandong University (62550089963197)financially supported by the National Natural Science Foundation of China (11701045)the Yangtze Youth Fund (2016cqn56)
文摘Let M be a C^(2)-smooth Riemannian manifold with boundary and X be a metric space with non-positive curvature in the sense of Alexandrov.Let u:M→X be a Sobolev mapping in the sense of Korevaar and Schoen.In this short note,we introduce a notion of p-energy for u which is slightly different from the original definition of Korevaar and Schoen.We show that each minimizing p-harmonic mapping(p≥2)associated to our notion of p-energy is locally Holder continuous whenever its image lies in a compact subset of X.
文摘蜘蛛作为草原生态系统中的主要消费者,对维系草原生物多样性和生态系统功能具有重大意义。放牧是人类利用草原最普遍的方式,了解放牧对蜘蛛多样性的影响具有重要生态学意义。本研究调查了内蒙古赛罕乌拉草原上5个不同放牧强度样地中的蜘蛛多样性,通过单因素方差分析(one-wayanalysisofvariance)比较各样地中的蜘蛛多样性,非度量多维标度分析(non-metric multidimensional scale,NMDS)和相似性分析(analysis of similarities,ANOSIM)比较各样地间的蜘蛛物种组成相似性,再结合相关性分析探讨了植被高度对蜘蛛多样性的影响。结果表明:重度放牧强度样地的蜘蛛多样性显著低于其他未放牧及轻度放牧样地;具体到常见科上,放牧强度对织网型的园蛛物种数和个体数影响显著,而对游猎型的狼蛛、跳蛛却不明显;织网型蜘蛛主要受植被结构影响,而游猎型蜘蛛更可能受潜在猎物可得性的影响。NMDS分析表明不同放牧强度下,蜘蛛类群的物种组成呈现明显的梯度变化,放牧强度越低,物种组成和未放牧样地越相近。相关性分析表明草原植被高度与蜘蛛多样性总体上呈正相关关系,即植被高度越高,蜘蛛多样性越高。其中依靠植物构建蛛网的园蛛科和在植物上层伏击猎物的蟹蛛科、逍遥蛛科等与植被高度显著相关。这说明植物资源及其空间异质性可能对草原蜘蛛多样性起着主导作用。因此,降低放牧强度有助于保护草原蜘蛛群落的多样性,特别有利于织网型蜘蛛。
