Title | Regularity estimates for scalar conservation laws in one space dimension |

Publication Type | Preprint |

2017 | |

Authors | Marconi, E |

Document Number | SISSA;37/2017/MATE |

In this paper we deal with the regularizing effect that, in a scalar conservation laws in one space dimension, the nonlinearity of the flux function ƒ has on the entropy solution. More precisely, if the set ⟨w : ƒ " (w) ≠ 0⟩ is dense, the regularity of the solution can be expressed in terms of BV Ф spaces, where Ф depends on the nonlinearity of ƒ. If moreover the set ⟨w : ƒ " (w) = 0⟩ is finite, under the additional polynomial degeneracy condition at the inflection points, we prove that ƒ' 0 u(t) ∈ BVloc (R) for every t > 0 | |

http://preprints.sissa.it/handle/1963/35291 |

## Regularity estimates for scalar conservation laws in one space dimension

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