Strong traces for solutions of $2\times 2$ nonlinear hyperbolic systems

In this paper we show that bounded entropy solutions of genuinely nonlinear $2\times 2$ systems of hyperbolic conservation laws admit a strong trace on Lipschitz curves. The main argument relies on a new half-space Liouville-type theorem for isentropic solutions with constant normal traces, providing the first extension to general genuinely nonlinear systems of the strong trace properties available for scalar conservation laws.