Skip to main content
SpringerLink
Log in

A Simple Diffractive Boundary Value Problem on an Asymptotically Anti-de Sitter Space

  • Conference paper
  • First Online:
Microlocal Methods in Mathematical Physics and Global Analysis

Part of the book series: Trends in Mathematics ((RESPERSP))

Abstract

In this project we study the propagation of singularities (in the sense of \({\mathcal{C}}^{\infty }\) wave front set) of the solution of a model case initial – boundary value problem with glancing rays for a concave domain on an asymptotically Anti de-Sitter manifold.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. L. Hörmander. On the existence and regularity of solutions of linear pseudo-differential equations. L’Enseignement Math. 17 (1971), 99–163.

    MATH  Google Scholar 

  2. L. Hörmander. The analysis of Linear Partial Differential Operators, vol 4. Springer - Verlag, 1983. 416–430.

    Google Scholar 

  3. G. Lebeau. Propagation des ondes dans les variétés à coins. Anns. Scient. Éc. Norm. Sup., 30:429–497, 19997

    Google Scholar 

  4. F.G. Friedlander. The wavefront set of the solution of a simple initial-boundary value problem with glancing rays. Math. Proc. Camb. Phil. 79 (1976), 145–159.

    Article  MATH  Google Scholar 

  5. R. B. Melrose. Microlocal parametrices for diffrative boundary value problems. Duke Mathematical Journal. 42–4 (1975), 605–635.

    Article  MathSciNet  Google Scholar 

  6. R. B. Melrose. Local Fourier-Airy Integral Operators. Duke Mathematical Journal. 42–4 (1975), 583–604.

    Article  MathSciNet  Google Scholar 

  7. R. B. Melrose and J. Sjöstrand. Singularities of boundary value problems I Comm. Pure Appl. Math, 31:593–67, 1978.

    Article  MATH  Google Scholar 

  8. R. B. Melrose and J. Sjöstrand. Singularities of boundary value problems II Comm. Pure Appl. Math, 35:129–168, 1982.

    Article  MATH  Google Scholar 

  9. M. Taylor. Grazing rays and reflection of singularities of solutions to wave equations. Comm. Pure. Appl. Math., 29:1–38, 1976.

    Article  MathSciNet  MATH  Google Scholar 

  10. A. Vasy. Propagation of singularities for the wave equation on manifold with corners. Annals of Mathematics 168 (2008) 749–812,

    Article  MathSciNet  MATH  Google Scholar 

  11. A. Vasy. The wave equation on asymptotically anti-de Sitter spaces To appear in Analysis and PDE.

    Google Scholar 

  12. K. Datchev and A. Vasy. Gluing semiclassical resolvent estimates via propagation of singularities (2010) preprint.

    Google Scholar 

  13. A. Vasy and M. Zworski. Semiclassical estimates in asymptotically Euclidean scattering Comm. Math. Phys. 212(1) : 205–217, 2007.

    MathSciNet  Google Scholar 

  14. R.B. Melrose, S.B. Antônio and A. Vasy. Analytic continuation and semiclassical resolvent estimates on asymptotically hyperbolic spaces (2010) preprint.

    Google Scholar 

Download references

Acknowledgements

I would like to thank my advisor András Vasy for all his help with this project.

Author information

Authors and Affiliations

  1. Purdue University, West Lafayette, IN, USA

    Ha Pham

Authors
  1. Ha Pham
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ha Pham .

Editor information

Editors and Affiliations

  1. Ammerländer Heerstr. 114-118, Oldenburg, 26111, Germany

    Daniel Grieser

  2. Inst. Mathematik, Universität Tübingen, Auf der Morgenstelle 10, Tübingen, 72076, Germany

    Stefan Teufel

  3. , Department of Mathematics, Bldg. 380, Stanford University, 450, Serra Mall, Stanford, 94305-2125, California, USA

    Andras Vasy

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer Basel

About this paper

Cite this paper

Pham, H. (2013). A Simple Diffractive Boundary Value Problem on an Asymptotically Anti-de Sitter Space. In: Grieser, D., Teufel, S., Vasy, A. (eds) Microlocal Methods in Mathematical Physics and Global Analysis. Trends in Mathematics(). Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0466-0_31

Download citation

Publish with us

Policies and ethics

Search

Navigation