Advertisement

Siberian Mathematical Journal

, Volume 59, Issue 6, pp 1024–1033 | Cite as

The Poincaré Inequality and p-Connectedness of a Stratified Set

  • N. S. DairbekovEmail author
  • O. M. Penkin
  • L. O. Sarybekova
Article
  • 7 Downloads

Abstract

We extend the Poincaré inequality to functions of Sobolev type on a stratified set. The integrability exponents in these analogs depend on the geometric characteristics of the stratified set which show to what extent their strata are connected with each other and the boundary. We apply the results to proving the solvability of boundary value problems for the p-Laplacian with boundary conditions of Neumann or Wentzel type.

Keywords

Poincaré inequality stratified set p-Laplacian 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Zhikov V. V., “Connectedness and homogenization. Examples of fractal conductivity,” Sb. Math., vol. 187, No. 8, 1109–1147 (1996).MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Kulyaba V. V. and Penkin O. M., “Strong stratified sets and the Friedrichs inequality,” Differ. Equ., vol. 40, No. 1, 75–82 (2004).MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Pham F., Introduction to the Topological Study of Landau Singularities [Russian translation], Mir, Moscow (1970).Google Scholar
  4. 4.
    Adams R. A., Sobolev Spaces, Acad. Press, New York (1975).zbMATHGoogle Scholar
  5. 5.
    Sobolev S. L., Some Applications of Functional Analysis in Mathematical Physics, Amer. Math. Soc., Providence (1991).zbMATHGoogle Scholar
  6. 6.
    Nazarov A. I. and Poborchii S. V., The Poincaré Inequality and Some of Its Applications [Russian], St. Petersburg Univ., St. Petersburg (2012).Google Scholar
  7. 7.
    Pokornyi Yu. V., Penkin O. M., Pryadiev V. L. et al., Differential Equations on Geometric Graphs [Russian], Fizmatlit, Moscow (2004).zbMATHGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  • N. S. Dairbekov
    • 1
    Email author
  • O. M. Penkin
    • 1
  • L. O. Sarybekova
    • 1
  1. 1.Kazakh-British Technical UniversityAlmatyKazakhstan

Personalised recommendations