Acta mathematica scientia,Series A ›› 2010, Vol. 30 ›› Issue (2): 425-431.

• Articles • Previous Articles     Next Articles

Local Boundedness Results Related to Anisotropic Functionals and Anisotropic Equations

 GAO Hong-YA1,2, WANG Hong-Min1, CHU Yu-Ming3   

  1. 1.College of Mathematics and Computer Science, Hebei University, Hebei Baoding 071002;
    2.Hebei Privincial Center of Mathematics, Shijiazhuang 050016;
    3.Faculty of Science, Huzhou Teachers College, Zhejiang Huzhou 313000
  • Received:2007-12-07 Revised:2008-09-29 Online:2010-04-25 Published:2010-04-25
  • Supported by:

    高红亚获河北省自然科学基金数学研究专项(07M003)资助; 褚玉明获973前期研究专项(2006708304), 国家自然科学基金(10771195)和浙江省自然科学基金(Y607128)资助.

Abstract:

Local boundedness results for minima of the anisotropic functional
I(u; Ω) = ∫Ω  f(x, u, Du)dx,  u ∈ Wloc1,(qi)(Ω),
and weak solutions of the anisotropic equation
div A(x, u, Du) =0,  u ∈ Wloc1,(qi)(Ω)
are proved, which can be regarded as generalizations of the classical results.

Key words: Local boundedness, Anisotropic functional, Anisotropic equation

CLC Number: 

  • 35J50
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