Uniqueness and existence of $L^$#x221E;$ solutions to initial boundary value problems for
scalar conservation laws, with continuous flux functions, is derived by $L^1$ contraction of Young
measure solutions. The classical Kruzkov entropies, extended in Bardos, LeRoux and Nedelec’s
sense to boundary value problems, are sufficient for the contraction. The uniqueness proof uses
the essence of Kruzkov’s idea with his symmetric entropy and entropy flux functions, but the usual
doubling of variables technique is replaced by the simpler fact that mollified measure solutions are
in fact smooth solutions. The mollified measures turn out to have not only weak but also strong
boundary entropy flux traces. Another advantage with the Young measure analysis is that the usual
assumption of Lipschitz continuous flux functions can be relaxed to continuous fluxes, with little
additional work.