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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
Article

Abstract

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).

Keywords

Radon Monotone Function Viscosity Solution Concave Function Jacobi Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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