2016/07/14 by Daniel Grieser, Grieser, Daniel · 2 citations
Mathematics · #35-02 (Primary) #35B25 #35P05 #58J37 (Secondary) #Analysis of PDEs (math.AP) #Analytic and geometric function theory #FOS: Mathematics #Nonlinear Partial Differential Equations #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.1607.04171
openalex publication_date 2016/07/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this expository article we show how the concepts of manifolds with corners, blow-ups and resolutions can be used effectively for the construction of quasimodes, i.e. approximate eigenfunctions of the Laplacian on certain families of spaces, mostly exemplified by domains Ωh⊂ℝ2, that degenerate as h→0. These include standard adiabatic limit families and also families that exhibit several types of scaling behavior. An introduction to manifolds with corners and resolutions, and how they relate to the idea of (multiple) scales and matching, is included.