Counter example to Strichartz estimates for the wave equation in domains

Oana Ivanovici (1)

1 LM-Orsay - Laboratoire de Mathématiques d'Orsay

Let U be a bounded, regular, strictly convex domain of R^2 and consider the wave equation on U with Dirichlet boundary condition. We prove that in such a domain the Strichartz estimates for the wave equation suffer losses when compared to the case U=R^2, at least for a subset of the usual range of indices.

Domaines: Equations aux dérivées partielles [math.AP]

Oana Ivanovici. Counter example to Strichartz estimates for the wave equation in domains. 2008. ⟨hal-00280810v2⟩