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非线性椭圆型偏微分方程弱解的存在性 被引量：3

The Existence of Weak Solutions for Nonlinear Elliptic Partial Differential Equations
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摘要 在W1,p(x)空间框架下研究了具有p(x)增长条件的椭圆型偏微分方程:-d iva(x,u,D u)+g(x,u,u)=f,得到了在W10,p(x)空间中弱解的存在性,推广了Boccardo等关于在Sobo lev空间中弱解的相应结论. In this paper the elliptic partial differential equations satisfying p（x） growth conditions： - diva（x,u,Du） ＋ g（x,u,↓△） = fare stadied in the setting of W^1,p（x） space, and the existence of weak solutions in W^10,p（x） is obtained which generalizes the corresponding work of Baccardo et al for the weak solutions in Sobolev space.
作者 孟晨辉 付永强
机构地区 哈尔滨工业大学数学系
出处 《应用泛函分析学报》 CSCD 2006年第1期21-27,共7页 Acta Analysis Functionalis Applicata
基金 国家自然科学基金(19971031)
关键词 椭圆型偏微分方程 弱解 存在性 elliptic partial differential equation existence weak solution
分类号 O175.2 [理学—基础数学]
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参考文献8

  • 1Boccardo L,Gallouet T,Murat F.A Unified Presentation of Two Existence Results for Problems with Natural Growth [A].M.Chipot.Progress in P.D.E.,the Metz surveys 2,Reseach Notes in Mathematics[C].New York,Longman,1993,296:127-137.
  • 2DONG,Zeng-fu(董增福),FU,Yong-qiang(付永强).Convergence of gradient of solutions to elliptic equations with nonuniform growth[J].Journal of Harbin Institute of Technology(New Series),2002,9(4):351-353. 被引量：2
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二级参考文献1

共引文献1

同被引文献20

  • 1RUZICKA M. Electrorheological fluids : modeling and mathematical theory[ M]. Berlin : Springer - Vedag, 2000.
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  • 6BOCCARDO L, GALLOUET T, ORSINA L. Existence and uniquness of entropy solutions for nonlinear elliptic equations with measure data[J]. Ann Inst H Poincare Anal Non Lineaire, 1993, 127:134 -156.
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  • 10KOVACIK O, RAKOSNIK J. On spaces Lp^(x) and W^kp(x) [ J]. Czechoslovak Math J, 1991, 41 : 592 - 618.

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应用泛函分析学报
2006年 第1期

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