Regularity of Solutions to Hamilton-Jacobi Equations

  • Andrea C. G. Mennucci
Part of the The Springer International Series in Engineering and Computer Science book series (SECS, volume 518)


We formulate a Hamilton-Jacobi partial differential equation H(x, Du(x)) = 0 on a n dimensional manifold M, with assumptions of uniform convexity of H(x,.)and regularity of H in a neighborhood of {H = 0} in T*M; we define the “min solution” u, a generalized solution, which often coincides with the viscosity solution; the definition is suited to proving regularity results about u; in particular, we prove that the closure of the set where u is not regular is a ℋn-1-rectifiable set.

Dedication: to Sanjoy, for the times he wasted listening to my wrong conjectures, for the times he spent listening to my right conjectures.


Viscosity Solution Symplectic Manifold Geometric Measure Theory Uniform Convexity Unique Viscosity Solution 
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Copyright information

© Springer Science+Business Media New York 2000

Authors and Affiliations

  • Andrea C. G. Mennucci
    • 1
  1. 1.Scuola Normale Superiore Piazza dei Cavalieri 7PisaItaly

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