Archive for Rational Mechanics and Analysis

, Volume 200, Issue 3, pp 1003–1021 | Cite as

SBV Regularity for Hamilton–Jacobi Equations in \({{\mathbb R}^n}\)

  • Stefano BianchiniEmail author
  • Camillo De Lellis
  • Roger Robyr


In this paper we study the regularity of viscosity solutions to the following Hamilton–Jacobi equations
$$\partial_{t}u+H(D_{x}u)=0\quad\hbox{in }\Omega\subset{\mathbb R}\times{\mathbb R}^{n}.$$
In particular, under the assumption that the Hamiltonian \({H\in C^2({\mathbb R}^n)}\) is uniformly convex, we prove that D x u and ∂ t u belong to the class SBV loc (Ω).


Radon Monotone Function Viscosity Solution Concave Function Jacobi Equation 
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Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  • Stefano Bianchini
    • 1
    Email author
  • Camillo De Lellis
    • 2
  • Roger Robyr
    • 2
  1. 1.SISSATriesteItaly
  2. 2.Institut für MathematikUniversität ZürichZürichSwitzerland

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