JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2020, Vol. 55 ›› Issue (2): 48-56.doi: 10.6040/j.issn.1671-9352.0.2019.408

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Global regularity for very weak solutions to non-homogeneous A-harmonic equation

XU Xiu-juan, YAN Shuo, ZHU Ye-qing   

  1. College of Science, North China University of Science and Technology, Tangshan 063210, Hebei, China
  • Published:2020-02-14

Abstract: This paper deals with boundary value problem for non-homogeneous A-harmonic equation div(A(x,∇u))=f(x). A global regularity result is derived for very weak solutions under some controllable and coercivity conditions and some proper integrable assumptions on the nonlinear term, by using the Hodge decomposition theorem and the methods in Sobolev spaces. The results generalize the corresponding results in related literatures.

Key words: A-harmonic equation, Hodge decomposition theorem, global regularity

CLC Number: 

  • O175.25
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