Regularity for anisotropic solutions to some nonlinear elliptic system

详细信息    查看全文

• 作者：Hongya Gao ; Shuang Liang ; Yi Cui
• 关键词：Regularity ; anisotropic solution ; nonlinear elliptic system ; 49N60 ; 35J60
• 刊名：Frontiers of Mathematics in China
• 出版年：2016
• 出版时间：February 2016
• 年：2016
• 卷：11
• 期：1
• 页码：77-87
• 全文大小：141 KB
• 参考文献：1.Gao H. Regularity for solutions to anisotropic obstacle problems. Sci China Math, 2014, 57: 111鈥?22MATH MathSciNet CrossRef
  2.Gao H, Chu Y. Quasiregular Mappings and A-Harmonic Equation. Beijing: Science Press, 2013 (in Chinese)
  3.Gao H, Di Q, Ma D. Integrability for solutions to some anisotropic obstacle problems. Manuscripta Math (to appear)
  4.Gao H, Huang Q. Local regularity for solutions of anisotropic obstacle problems. Nonlinear Anal, 2012, 75: 4761鈥?765MATH MathSciNet CrossRef
  5.Gao H, Liu C, Tian H. Remarks on a paper by Leonetti and Siepe. J Math Anal Appl, 2013, 401: 881鈥?87MATH MathSciNet CrossRef
  6.Giachetti D, Porzio M M. Local regularity results for minima of functionals of the calculus of variation. Nonlinear Anal, 2000, 39: 463鈥?82MATH MathSciNet CrossRef
  7.Giaquinta M. Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems. Ann of Math Stud, Vol 105. Princeton: Princeton University Press, 1983MATH
  8.De Giorgi E. Un esempio di estremali discontinue per un problema variazionale di tipo ellittico. Boll Unione Mat Ital, 1968, 4: 135鈥?37
  9.Leonetti F, Mascolo E. Local boundedness for vector valued minimizers of anisotropic functionals. Z Anal Anwend, 2012, 31: 357鈥?78MATH MathSciNet CrossRef
  10.Leonetti F, Petricca P V. Regularity for vector valued minimizers of some anisotropic integral functionals. J Inequal Pure Appl Math, 2006, 7(3): Art 88MathSciNet
  11.Leonetti F, Petricca P V. Existence of bounded solutions to some nonlinear degenerate elliptic systems. Discrete Contin Dyn Syst Ser B, 2009, 11: 191鈥?03MATH MathSciNet
  12.Leonetti F, Siepe F. Integrability for solutions to some anisotropic elliptic equations. Nonlinear Anal, 2012, 75: 2867鈥?873MATH MathSciNet CrossRef
  13.Leonetti F, Siepe F. Global integrability for minimizers of anisotropic functionals. Manuscripta Math, 2014, 144: 91鈥?8MATH MathSciNet CrossRef
  14.Mingione G. Regularity of minima: an invitation of dark side of the calculus of variations. Appl Math, 2006, 51: 355鈥?26MATH MathSciNet CrossRef
  15.Stampacchia G. Equations Elliptiques du second ordre a coefficientes discontinus. Semin de Math Superieures, Univ de Montreal, 1996
  16.Stroffolini B. Global boundedness of solutions of anisotropic variational problems. Boll Unione Mat Ital, 1991, 5A: 345鈥?52MathSciNet
  17.Tang Q. Regularity of minimizers of non-isotropic integrals of the calculus of variations. Ann Mat Pura Appl, 1993, 164: 77鈥?7MATH MathSciNet CrossRef
  18.Zhou S. A note on nonlinear elliptic systems involving measure. Electron J Differential Equations, 2000, (08): 1鈥?
  
• 作者单位：Hongya Gao (1)
  Shuang Liang (1)
  Yi Cui (1)
  
  1. College of Mathematics and Information Science, Hebei University, Baoding, 071002, China
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Chinese Library of Science
  
• 出版者：Higher Education Press, co-published with Springer-Verlag GmbH
• ISSN：1673-3576

文摘

This paper deals with anisotropic solutions \(u \in W^{1,(p_i )} (\Omega ,\mathbb{R}^N )\) to the nonlinear elliptic system $$ - \sum\limits_{i = 1}^n {D_i (a_i^\alpha (x,Du(x)))} = - \sum\limits_{i = 1}^n {D_i F_i^\alpha (x)} ,\alpha = 1,2,...,N$$