Skip to main content

Boundary Value Problems in Boutet de Monvel’s Calculus on Manifolds with Edge

  • Conference paper
  • First Online:
  • 314 Accesses

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 276))

Abstract

The present exposition is a contribution to the third conference AMINSE. Our topic is related to research teams from the I. Vekua Institute of Applied Mathematics and Iv. Javakhishvili Tbilisi State University who are working in the tradition of I. Vekua. The authors are happy to give an overview of in memory of Professor David Gordeziani who contributed so much for building up mathematical institutions in Tbilisi to attractive centers of research in many areas, including singular analysis, with members Jaiani, Chinchaldze, Duduchava, Natroshvili and many others.

Dedicated to the Memory of Prof. Dr. David Gordeziani

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD   109.99
Price excludes VAT (USA)
  • Durable hardcover 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

Learn about institutional subscriptions

References

  1. Agranovich, M.S., Vishik, M.I.: Elliptic problems with parameter and parabolic problems of general type. Uspekhi Mat. Nauk 19(3), 53–161 (1964)

    MathSciNet  MATH  Google Scholar 

  2. Boutet de Monvel, L.: Boundary problems for pseudo-differential operators. Acta Math. 126, 11–51 (1971)

    Article  MathSciNet  Google Scholar 

  3. Egorov, J.V., Schulze, B.-W.: Pseudo-differential operators, singularities, applications. Oper. Theory Adv. Appl. 93 (1997). Birkhäuser Verlag, Basel

    Google Scholar 

  4. Eskin, G.I.: Boundary value problems for elliptic pseudodifferential equations. Trans. Nauka Moskva (1973). Math. Monogr. Amer. Math. Soc. 52, Providence, Rhode Island (1980)

    Google Scholar 

  5. Khalil, S., Schulze, B.-W.: Boundary problems on a manifold with edge. Asian-Eur. J. Math. (AEJM) 10 (2), 1750087 (2017). (43 pages). https://doi.org/10.1142/S1793557117500875

    Article  MathSciNet  Google Scholar 

  6. Khalil, S., Schulze, B.-W.: Calculus on a Manifold with Edge and Boundary (in preparation)

    Google Scholar 

  7. Kondratyev, V.A.: Boundary value problems for elliptic equations in domains with conical points. Trudy Mosk. Mat. Obshch. 16, 209–292 (1967)

    MathSciNet  Google Scholar 

  8. Krainer, T.: Parabolic pseudo-differential operators and long-time asymptotics of solutions. Ph.D. thesis, University of Potsdam (2000)

    Google Scholar 

  9. Liu, X., Schulze, B.-W.: Boundary value problems in edge representation. Math. Nachr. 280, 5–6 (2007)

    Article  MathSciNet  Google Scholar 

  10. Rempel, S., Schulze, B.-W.: Index Theory of Elliptic Boundary Problems. Akademie-Verlag, Berlin (1982). North Oxford Acad. Publ. Comp., Oxford (1985). (Transl. to Russian: Mir, Moscow (1986))

    Google Scholar 

  11. Schrohe, E., Schulze, B.-W.: Boundary value problems in Boutet de Monvel’s calculus for manifolds with conical singularities I. Advances in Partial Differential Equations “Pseudo-Differential Calculus and Mathematical Physics”, pp. 97–209. Akademie Verlag, Berlin (1994)

    Google Scholar 

  12. Schrohe, E., Schulze, B.-W.: Boundary value problems in Boutet de Monvel’s calculus for manifolds with conical singularities II. Advances in Partial Differential Equations “Boundary Value Problems. Schrödinger Operators, Deformation Quantization”, pp. 70–205. Akademie Verlag, Berlin (1995)

    Google Scholar 

  13. Schulze, B.-W.: Boundary Value Problems and Singular Pseudo-differential Operators. Wiley, Chichester (1998)

    MATH  Google Scholar 

  14. Schulze, B.-W., Seiler, J.: Elliptic complexes on manifolds with boundary. J. Geom. Anal. (2018, to appear)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Sara Khalil .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Khalil, S., Schulze, BW. (2019). Boundary Value Problems in Boutet de Monvel’s Calculus on Manifolds with Edge. In: Jaiani, G., Natroshvili, D. (eds) Mathematics, Informatics, and Their Applications in Natural Sciences and Engineering. AMINSE 2017. Springer Proceedings in Mathematics & Statistics, vol 276. Springer, Cham. https://doi.org/10.1007/978-3-030-10419-1_8

Download citation

Publish with us

Policies and ethics