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高校应用数学学报
Applied Mathematics A Journal of Chinese Universities  2015, Vol. 30 Issue (4): 399-409    DOI:
    
Regularity of the solutions to fourth order elliptic equations in general domains
QI Hong-hong, JIA Gao, LIU Wei
College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China
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Abstract  Based on new integral estimates, the regularity of the solutions of fourth order elliptic equations in arbitrary three-dimensional domains is studied. The boundedness of the gradient of the solutions is obtained.

Key words： fourth-order elliptic equation      gradient      boundedness     
Received: 31 December 2014      Published: 19 May 2018
CLC:  O175.25  
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QI Hong-hong
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LIU Wei
Cite this article:

QI Hong-hong, JIA Gao, LIU Wei. Regularity of the solutions to fourth order elliptic equations in general domains. Applied Mathematics A Journal of Chinese Universities, 2015, 30(4): 399-409.

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http://www.zjujournals.com/amjcua/     OR     http://www.zjujournals.com/amjcua/Y2015/V30/I4/399


任意区域上一类四阶椭圆方程解的正则性

根据新的积分估计, 在任意三维区域中, 研究一类四阶椭圆方程解的正则性, 得到解的梯度几乎处处有界的结论.

关键词： 四阶椭圆方程,  梯度,  有界性 
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[2] QI Hong-hong, JIA Gao. Multiplicity of solutions for a class of quasilinear elliptic equations with periodic variable exponents and concave-convex nonlinearities[J]. Applied Mathematics A Journal of Chinese Universities, 2016, 31(3): 294-306.