TY - GEN
T1 - Fractional spaces and conservation laws
AU - Castelli, Pierre
AU - Jabin, Pierre Emmanuel
AU - Junca, Stéphane
N1 - Publisher Copyright:
© Springer International Publishing AG, part of Springer Nature 2018.
PY - 2018
Y1 - 2018
N2 - In 1994, Lions, Perthame and Tadmor conjectured the maximal smoothing effect for multidimensional scalar conservation laws in Sobolev spaces. For strictly smooth convex flux and the one-dimensional case, we detail the proof of this conjecture in the framework of Sobolev fractional spaces Ws,1, and in fractional BV spaces: BVs. The BVs smoothing effect is more precise and optimal. It implies the optimal Sobolev smoothing effect in Ws,1 and also in Ws,p with the optimal p=1/s. Moreover, the proof expounded does not use the Lax–Oleinik formula but a generalized one-sided Oleinik condition.
AB - In 1994, Lions, Perthame and Tadmor conjectured the maximal smoothing effect for multidimensional scalar conservation laws in Sobolev spaces. For strictly smooth convex flux and the one-dimensional case, we detail the proof of this conjecture in the framework of Sobolev fractional spaces Ws,1, and in fractional BV spaces: BVs. The BVs smoothing effect is more precise and optimal. It implies the optimal Sobolev smoothing effect in Ws,1 and also in Ws,p with the optimal p=1/s. Moreover, the proof expounded does not use the Lax–Oleinik formula but a generalized one-sided Oleinik condition.
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U2 - 10.1007/978-3-319-91545-6_23
DO - 10.1007/978-3-319-91545-6_23
M3 - Conference contribution
AN - SCOPUS:85049372807
SN - 9783319915449
T3 - Springer Proceedings in Mathematics and Statistics
SP - 285
EP - 293
BT - Theory, Numerics and Applications of Hyperbolic Problems I - Aachen, Germany, 2016
A2 - Westdickenberg, Michael
A2 - Klingenberg, Christian
PB - Springer New York LLC
T2 - 16th International Conference on Hyperbolic Problems: Theory, Numerics and Applications, 2016
Y2 - 1 August 2016 through 5 August 2016
ER -