On the sharp regularity of solutions to hyperbolic boundary value problems
[Régularité précise pour les solutions de problèmes aux limites hyperboliques]
Audiard, Corentin1
1 LJLL / UMR 5208, 4 place Jussieu, 75252 Paris Cedex 5, France
Annales Henri Lebesgue, Tome 6 (2023), pp. 1349-1369

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+ℕ, as it involves nonlocal compatibility conditions.

Des résultats de régularité optimaux sont prouvés pour une famille de problèmes aux limites hyperboliques du premier ordre. Nos deux principales améliorations sur la littérature classique sont un affaiblissement de la régularité requise des conditions au bord, et des résultats de régularité dans des espaces de Sobolev fractionnaires. Ce dernier point est particulièrement intéressant lorsque l’indice de régularité est dans 1/2+ℕ, car il fait apparaître des conditions de compatibilité non locales.

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DOI : 10.5802/ahl.190
Classification : 35L04, 35B65
Keywords: Boundary value problems, hyperbolic problems, regularity of solutions, interpolation

Audiard, Corentin 1

1 LJLL / UMR 5208, 4 place Jussieu, 75252 Paris Cedex 5, France
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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Audiard, Corentin. On the sharp regularity of solutions to hyperbolic boundary value problems. Annales Henri Lebesgue, Tome 6 (2023), pp. 1349-1369. doi: 10.5802/ahl.190

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