01221nas a2200097   4500008004100000245007700041210006900118520087000187100001801057856004801075       2017                        en  d00aRegularity estimates for scalar conservation laws in one space dimension0 aRegularity estimates for scalar conservation laws in one space d3 aIn 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
and that this can be improved to SBVloc (R) regularity except an at most countable set of singular times. Finally we present some examples that shows the sharpness of these results and counterexamples to related questions, namely regularity in the kinetic formulation and a property of the fractional BV spaces.1 aMarconi, Elio  uhttp://preprints.sissa.it/handle/1963/35291