Open Access

Boundary regularity of weak solutions to nonlinear elliptic obstacle problems

Boundary Value Problems20062006:72012

DOI: 10.1155/BVP/2006/72012

Received: 25 April 2005

Accepted: 14 September 2005

Published: 15 February 2006


We study the boundary regularity of weak solutions to nonlinear obstacle problem with -obstacle function, and obtain the boundary regularity.


Authors’ Affiliations

College of Mathematics and Computer Science, Hebei University
College of Science, Huzhou University


  1. Adams DR: Capacity and the obstacle problem. Applied Mathematics and Optimization. An International Journal 1982,8(1):39–57.MathSciNetView ArticleMATHGoogle Scholar
  2. Chiacchio F: Regularity for solutions of nonlinear elliptic equations with natural growth in the gradient. Bulletin des Sciences Mathématiques 2000,124(1):57–74.MathSciNetView ArticleMATHGoogle Scholar
  3. Choe HJ: A regularity theory for a general class of quasilinear elliptic partial differential equations and obstacle problems. Archive for Rational Mechanics and Analysis 1991,114(4):383–394. 10.1007/BF00376141MathSciNetView ArticleMATHGoogle Scholar
  4. Choe HJ, Lewis JL: On the obstacle problem for quasilinear elliptic equations of Laplacian type. SIAM Journal on Mathematical Analysis 1991,22(3):623–638. 10.1137/0522039MathSciNetView ArticleMATHGoogle Scholar
  5. Evans LC: Partial Differential Equations, Graduate Studies in Mathematics. Volume 19. American Mathematical Society, Rhode Island; 1998:xviii+662.Google Scholar
  6. Fuchs M: Hölder continuity of the gradient for degenerate variational inequalities. Nonlinear Analysis. Theory, Methods & Applications. An International Multidisciplinary Journal. Series A: Theory and Methods 1990,15(1):85–100.MathSciNetView ArticleMATHGoogle Scholar
  7. Giaquinta M: Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems, Annals of Mathematics Studies. Volume 105. Princeton University Press, New Jersey; 1983:vii+297.Google Scholar
  8. Heinonen J, Kilpeläinen T: On the Wiener criterion and quasilinear obstacle problems. Transactions of the American Mathematical Society 1988,310(1):239–255. 10.1090/S0002-9947-1988-0965751-8MathSciNetView ArticleMATHGoogle Scholar
  9. Lieberman GM: The natural generalization of the natural conditions of Ladyzhenskaya and Ural'tseva for elliptic equations. Communications in Partial Differential Equations 1991,16(2–3):311–361. 10.1080/03605309108820761MathSciNetView ArticleMATHGoogle Scholar
  10. Lindqvist P: Regularity for the gradient of the solution to a nonlinear obstacle problem with degenerate ellipticity. Nonlinear Analysis. Theory, Methods & Applications. An International Multidisciplinary Journal. Series A: Theory and Methods 1988,12(11):1245–1255.MathSciNetView ArticleGoogle Scholar
  11. Michael JH, Ziemer WP: Interior regularity for solutions to obstacle problems. Nonlinear Analysis. Theory, Methods & Applications. An International Multidisciplinary Journal. Series A: Theory and Methods 1986,10(12):1427–1448.MathSciNetView ArticleMATHGoogle Scholar
  12. Mu J: Higher regularity of the solution to the -Laplacian obstacle problem. Journal of Differential Equations 1992,95(2):370–384. 10.1016/0022-0396(92)90036-MMathSciNetView ArticleMATHGoogle Scholar
  13. Tan Z, Yan ZQ: Regularity of weak solutions to some degenerate elliptic equations and obstacle problems. Northeastern Mathematical Journal. Dongbei Shuxue 1993,9(2):143–156.MathSciNetMATHGoogle Scholar
  14. Yang J: Regularity of weak solutions to quasilinear elliptic obstacle problems. Acta Mathematica Scientia. Series B. English Edition 1997,17(2):159–166.MathSciNetMATHGoogle Scholar
  15. Zheng SZ: Partial regularity of -harmonic systems of equations and quasiregular mappings. Chinese Annals of Mathematics. Series A. Shuxue Niankan. A Ji 1998,19(1):63–72. translation in Chinese Journal of Contemporary Mathematics 19 (1998), no. 1, 19–30MathSciNetMATHGoogle Scholar


© Junxia and Yuming 2006

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.