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Sobolev met Poincaré

About this Title

Piotr Hajłasz and Pekka Koskela

Publication: Memoirs of the American Mathematical Society
Publication Year 2000: Volume 145, Number 688
ISBNs: 978-0-8218-2047-6 (print); 978-1-4704-0279-2 (online)
MathSciNet review: 1683160
MSC: Primary 46E35; Secondary 30C65, 31C25, 53C17, 58J60

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Table of Contents


  • 1. Introduction
  • 2. What are Poincaré and Sobolev inequalities?
  • 3. Poincaré inequalities, pointwise estimates, and Sobolev classes
  • 4. Examples and necessary conditions
  • 5. Sobolev type inequalities by means of Riesz potentials
  • 6. Trudinger inequality
  • 7. A version of the Sobolev embedding theorem on spheres
  • 8. Rellich-Kondrachov
  • 9. Sobolev classes in John domains
  • 10. Poincaré inequality: examples
  • 11. Carnot-Carathéodory spaces
  • 12. Graphs
  • 13. Applications to P.D.E and nonlinear potential theory
  • 14. Appendix