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非线性椭圆障碍问题弱解的内部正则性(英文) 被引量：2

Interior Regularity of Weak Solutions to Nonlinear Elliptic Obstacle Problems
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摘要 我们讨论具有C1,β障碍函数的非线性障碍问题弱解的内部正则性,得到了C1lo,cα的正则性结果. We study the interior regularity of weak solutions to a nonlinear obstacle problem with C1β obstacle function,and obtain the Cloc^1α regularity.
作者 孟俊霞 褚玉明
机构地区 河北大学数学与计算机学院 湖州师范学院数学系
出处 《应用数学》 CSCD 北大核心 2007年第1期171-182,共12页 Mathematica Applicata
基金 Supported by the Natural Science Foundation of Hebei University,the NationalNatural Science Foundation of China(10471039),the Zhejiang Provincial Natural Science Foundationof China(M103087)
关键词 内部正则性 弱解 障碍问题 Interior regularity Weak solution Obstacle problem
分类号 O178 [理学—基础数学]
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参考文献10

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同被引文献14

  • 1Ruzicka M. Electrorheological fluids: modeling and mathematical theory[C]//Lecture Notes in Mathe- matics 1748. Berlin : Springer-Verlag, 2000.
  • 2C HEN Y unmei,Levine S, Rao M. Variable exponent,linear growth functionals in image restoration[J]. SIAM J. Appl. Math., 2006,66 (4) : 1383-1406.
  • 3Zhikov V V. Averaging of functionals of the calculus of variations and elasticity theory[J]. Math. USSR Izvestiya, 1987,29 :33-36.
  • 4FAN Xianling. Solutions for p(x) -Laplacian Dirichlet problems with singular coecients[j]. J. Math. A- nal. Appl. , 2005,312 : 464-477.
  • 5Diening L. Riesz potential and Sobolev embeddings on generalized Lebesgue and Sobolev space L^p(*) and W^k,p(*) [J]. Math. Naehr. , 2004,268 : 31-43.
  • 6ZHANG Qihu. Boundary blow-up solutions to p(x) -Laplacian equations with exponential nonlinearities [J]. J. Inequal. Appl. , 2008 (2008), Article ID: 279306.
  • 7GAO Hongya, QIAO Jinjing, CHU Yuming. Local regularity and local boundedness results for very weak solutions of obstacle problems [J]. Journal of Inequalities and Applications, Volume 2010, Article ID 878769,12 pages,doi: 10. 1155/2010/878769.
  • 8Benilan Ph, Boccardo L, Gallouet T, Gariepy R, Pierre M, Vazquez J L. An L^1 -theory of existence and u- niqueness of solutions of nonlinear elliptic equations[J]. Ann. Sc. Norm. Super. Pisa, Cl. Sci. , 1995,22: 241-273.
  • 9Sanchon M, Urbano J M. Entropy solutions for the p(x) -Laplace equation[J]. Trans. Amer. Math. Soc., 2009,361 : 6387-6405.
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应用数学
2007年 第1期

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