REGULARITY OF P-HARMONIC MAPPINGS INTO NPC SPACES

Let M be a C²-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.     

SHARP MORREY REGULARITY THEORY FOR A FOURTH ORDER GEOMETRICAL EQUATION

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-Riviere 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 biharmonic mappings.Our results deepens the L^p type regularity theory of [10...     

三维稳态磁流体动力学方程的Liouville定理

研究了三维稳态磁流体动力学方程的Liouville定理.首先由能量估计建立了一个Caccioppoli型不等式，再结合Sobolev嵌入得到了Liouville定理成立的3个充分条件，其中一个充分条件表明：若三维稳态磁流体动力学方程的光滑解(u,b)∈L^p,3/2相似文献