Advertisement

Journal of Mathematical Sciences

, Volume 156, Issue 4, pp 569–576 | Cite as

Boundary estimates for solutions to the two-phase parabolic obstacle problem

  • D. E. Apushkinskaya
  • N. N. Uraltseva
Article
  • 25 Downloads

Estimates for the second-order derivatives of a solution to the two-phase parabolic obstacle problem are established. Similar results in the elliptic case were obtained by the authors in 2006. Bibliography: 4 titles.

Keywords

Obstacle Problem Sobolev Norm Arbitrary Direction Boundary Estimate Singular Perturbation Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    D. E. Apushkinskaya, N. N. Uraltseva, “Boundary estimates for solutions of two-phase obstacle problems” [in Russian], Probl. Math. Anal. 34 (2006), 3–11; English transl.: J. Math. Sci. (New York) 142 (2007), 1723–1732.Google Scholar
  2. 2.
    L. A. Caffarelli, C. Kenig, “Gradient estimates for variable coefficient parabolic equations and singular perturbation problems,” Amer. J. Math. 120 (1998), 391–439.MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    H. Shahgholian, N. Uraltseva, G. Weiss, The Parabolic Two-Phase Membrane Problem: Regularity in Higher Dimensions, Preprint, http://www.citebase.org/abstract?id=oai:arXiv.org:0712.3411, 2007.
  4. 4.
    N. N. Uraltseva, “Boundary estimates for solutions of elliptic and parabolic equations with discontinuous nonlinearities,” In: Nonlinear Equations and Spectral Theory, Am. Math. Soc. Transl. (2) 220 (2007), 235–246.Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2009

Authors and Affiliations

  1. 1.Universitat des SaarlandesSaarbrückenGermany
  2. 2.St. Petersburg State UniversitySt. PetersburgRussia

Personalised recommendations