Skip to main content

Transport Rays and Applications to Hamilton–Jacobi Equations

  • 1948 Accesses

Part of the Lecture Notes in Mathematics book series (LNMCIME,volume 2028)

Abstract

The aim of these notes is to introduce the readers to the use of the Disintegration Theorem for measures as an effective tool for reducing problems in transport equations to simpler ones. The basic idea is to partition Rd into one dimensional sets, on which the problem under consideration becomes one space dimensional (and thus much easier, hopefully).

Keywords

  • Jacobi Equation
  • Maximal Monotone Operator
  • Unique Disintegration
  • Optimal Couple
  • Measure Algebra

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.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   44.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   59.95
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. L. Ambrosio, N. Fusco, D. Pallara, Functions of bounded variation and free discontinuity problems (Oxford Mathematical Monographs, 2000)

    Google Scholar 

  2. F. Aubin, A. Cellina, Differential inclusions, set-valued maps and viability theory (Springer, New York, 1984)

    MATH  Google Scholar 

  3. S. Bianchini, C. De Lellis, R. Robyr, SBV regularity for Hamilton–Jacobi equations in d, Arch. Rational Mech. Anal. 200, 1003–1021 (2011) DOI: 10.1007/s00205-010-0381-z

    CrossRef  MATH  Google Scholar 

  4. S. Bianchini, M. Gloyer, On the Euler–Lagrange equation for a variational problem: the general case II. Math. Z. 265, 889–923 (2010) DOI: 10.1007/s00209-009-0547-2

    CrossRef  MathSciNet  MATH  Google Scholar 

  5. P. Cannarsa, A. Mennucci, C. Sinestrari, Regularity results for solutions of a class of Hamilton–Jacobi equations. Arch. Rational Mech. Anal. 140, 197–223 (1997)

    CrossRef  MathSciNet  MATH  Google Scholar 

  6. D.H. Fremlin, Measure Theory, vol. 3, Measure Algebras. (Torres Fremlin, 2004)

    Google Scholar 

  7. D.H. Fremlin, Measure Theory, vol. 4, Topological Measure Spaces. (Torres Fremlin, 2006)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Stefano Bianchini .

Rights and permissions

Reprints and Permissions

Copyright information

© 2011 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Bianchini, S., Gloyer, M. (2011). Transport Rays and Applications to Hamilton–Jacobi Equations. In: Nonlinear PDE’s and Applications. Lecture Notes in Mathematics(), vol 2028. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21861-3_1

Download citation