Homogenization of viscous and non-viscous HJ equations: a remark and an application

Homogenization of viscous and non-viscous HJ equations: a remark and an application It was pointed out by P.-L. Lions, G. Papanicolaou, and S.R.S. Varadhan in their seminal paper (1987) that, for first order Hamilton–Jacobi (HJ) equations, homogenization starting with affine initial data implies homogenization for general uniformly continuous initial data. The argument makes use of some properties of the HJ semi-group, in particular, the finite speed of propagation. This property is lost for viscous HJ equations. In this paper we prove the above mentioned implication in both viscous and non-viscous cases. Our proof relies on a variant of Evans’s perturbed test function method. As an application, we show homogenization in the stationary ergodic setting for viscous and non-viscous HJ equations in one space dimension with non-convex Hamiltonians of specific form. The results are new in the viscous case. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Calculus of Variations and Partial Differential Equations Springer Journals

Homogenization of viscous and non-viscous HJ equations: a remark and an application

Loading next page...
Springer Berlin Heidelberg
Copyright © 2017 by Springer-Verlag Berlin Heidelberg
Mathematics; Analysis; Systems Theory, Control; Calculus of Variations and Optimal Control; Optimization; Theoretical, Mathematical and Computational Physics
Publisher site
See Article on Publisher Site


You’re reading a free preview. Subscribe to read the entire article.

DeepDyve is your
personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

Enjoy affordable access to
over 12 million articles from more than
10,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

Unlimited reading

Read as many articles as you need. Full articles with original layout, charts and figures. Read online, from anywhere.

Stay up to date

Keep up with your field with Personalized Recommendations and Follow Journals to get automatic updates.

Organize your research

It’s easy to organize your research with our built-in tools.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

See the journals in your area

Monthly Plan

  • Read unlimited articles
  • Personalized recommendations
  • No expiration
  • Print 20 pages per month
  • 20% off on PDF purchases
  • Organize your research
  • Get updates on your journals and topic searches


Start Free Trial

14-day Free Trial

Best Deal — 39% off

Annual Plan

  • All the features of the Professional Plan, but for 39% off!
  • Billed annually
  • No expiration
  • For the normal price of 10 articles elsewhere, you get one full year of unlimited access to articles.



billed annually
Start Free Trial

14-day Free Trial