Counter example to Strichartz estimates for the wave equation in domains
Analysis of PDEs
2009-04-30 v2
Abstract
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.
Cite
@article{arxiv.0805.2901,
title = {Counter example to Strichartz estimates for the wave equation in domains},
author = {Oana Ivanovici},
journal= {arXiv preprint arXiv:0805.2901},
year = {2009}
}