On the sharp regularity of solutions to hyperbolic boundary value problems
Annales Henri Lebesgue, Volume 6 (2023), pp. 1349-1369.


Keywords Boundary value problems, hyperbolic problems, regularity of solutions, interpolation


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 1/2+, as it involves nonlocal compatibility conditions.


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