We prove some sharp regularity results for solutions of classical first order hyperbolic initial boundary value problems. Our two main improvements on the existing literature are weaker regularity assumptions for the boundary data and regularity in fractional Sobolev spaces. This last point is specially interesting when the regularity index belongs to , as it involves nonlocal compatibility conditions.
[Mét01] Stability of multidimensional shocks, Advances in the theory of shock waves (Progress in Nonlinear Differential Equations and their Applications), Volume 47, Birkhäuser, 2001, pp. 25-103 | DOI | MR | Zbl