On the maximal smoothing effect for multidimensional scalar conservation laws. (May 2017) - Castelli, Pierre; Junca, Stéphane
Abstract: In 1994, Lions, Perthame and Tadmor conjectured an optimal smoothing effect for entropy solutions of multidimensional scalar conservation laws. This effect estimated in fractional Sobolev spaces is linked to the flux nonlinearity. We use a new definition of a nonlinear smooth flux in order to show that the conjectured smoothing effect cannot be exceeded. First one-dimensional solutions are considered in fractional B V spaces. Then the multidimensional case is handled with a monophase solution.