Dispersion for the wave equation inside strictly convex domains I: the Friedlander model case

• 成果类型: Article
• 署名作者: Ivanovici, Oana; Lebeau, Gilles; Planchon, Fabrice
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2014.180.1.7
• 发表日期: 2014
• 页码: 323-380
• 关键词: compact manifolds; SINGULARITIES; parametrix; Operators

摘要

We consider a model case for a strictly convex domain Omega subset of R-d of dimens ion d >= 2 with smooth boundary partial derivative Omega not equal 0,and we describe dispersion for the wave equation with Dirichlet boundary conditions. More specifically, we obtain the optimal fixed time decay rate for the smoothed out Green function: at l(1/4) loss occurs with respect to the boundary less case,due to repeated occurrences of swallowtail type singularities in the wave front set. :