Regularity Results for Solutions of a Class of Hamilton-Jacobi Equations
- Cite this article as:
- Cannarsa, P., Mennucci, A. & Sinestrari, C. Arch Rational Mech Anal (1997) 140: 197. doi:10.1007/s002050050064
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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.