In this chapter, the wave equation is considered, at all times t∈ ℝ, in a domain G⊂ ℝn. The boundary ∂G contains finitely many smooth edges ℳm of various dimensions 0 ≤ dim ℳm≤ n− 2 ; outside of the union of edges, the boundary is smooth. The Dirichlet or Neumann conditions are given on ∂G∖ ∪ mm. We use this problem to demonstrate the method of combined estimates and derive the asymptotics of solutions near the edges.

Original languageEnglish
Title of host publicationAsymptotic Theory of Dynamic Boundary Value Problems in Irregular Domains
PublisherSpringer Nature
Pages13-73
Number of pages61
DOIs
StatePublished - 2021

Publication series

NameOperator Theory: Advances and Applications
Volume284
ISSN (Print)0255-0156
ISSN (Electronic)2296-4878

    Scopus subject areas

  • Analysis

ID: 77222201