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

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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).

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Authors and Affiliations

  1. SISSA, via Bonomea 265, 34136, Trieste, Italy

    Stefano Bianchini

  2. Institut für Mathematik, Universität Zürich, Winterthurerstrasse 190, 8057, Zürich, Switzerland

    Camillo De Lellis & Roger Robyr

Authors
  1. Stefano Bianchini
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  2. Camillo De Lellis
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  3. Roger Robyr
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Correspondence to Stefano Bianchini.

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Communicated by S. Bianchini

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Bianchini, S., De Lellis, C. & Robyr, R. SBV Regularity for Hamilton–Jacobi Equations in \({{\mathbb R}^n}\) . Arch Rational Mech Anal 200, 1003–1021 (2011). https://doi.org/10.1007/s00205-010-0381-z

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  • DOI: https://doi.org/10.1007/s00205-010-0381-z

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