, Volume 140, Issue 3, pp 197-223

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

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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 ℋ n ‐rectifiable set. In particular, it follows that Du belongs to the classSBV, i.e., D 2 u$ is a measure with no Cantor part.