Archive for Rational Mechanics and Analysis

, Volume 140, Issue 3, pp 197–223 | Cite as

Regularity Results for Solutions of a Class of Hamilton-Jacobi Equations

  • Piermarco Cannarsa
  • Andrea Mennucci
  • Carlo Sinestrari
Article

Abstract.

The regularity of the gradient of viscosity solutions of first‐order Hamilton‐Jacobi equations \(\) is studied under a strict convexity assumption on H(t,x,⋅). Estimates on the discontinuity set of Du are derived. Such estimates imply that solutions of the above problem are smooth in the complement of a closed ℋn‐rectifiable set. In particular, it follows that Du belongs to the classSBV, i.e., D2u$ is a measure with no Cantor part.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Piermarco Cannarsa
    • 1
  • Andrea Mennucci
    • 2
  • Carlo Sinestrari
    • 1
  1. 1.Dipartimento di Matematica, Università di Roma “Tor Vergata”, Via della Ricerca Scientifica, I‐00133 Roma, ItalyIT
  2. 2.Scuola Normale Superiore, Piazza dei Cavalieri, I‐56126 Pisa, ItalyIT

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