Skip to main content

The properness of elliptic and parabolic differential operators

Part of the Lecture Notes in Mathematics book series (LNM,volume 1453)

Keywords

  • Elliptic Equation
  • Proper Mapping
  • Positive Imaginary Part
  • Holder Space
  • Fredholm Mapping

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   34.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   46.00
Price excludes VAT (Canada)
  • 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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Zvyagin V.G. On the number of solutions to certain boundary-value problems.-Global analysis and mathematical physics. Voronezh, 1987 (in Russian).

    Google Scholar 

  2. Borisovich Yu.G., Zvyagin V.G., and Sapronov Yu.I. Non-linear Fredholm mappings and Leray-Schauder theory.-Usp. Matem. Nauk 1977, v. 32, No. 4 (in Russian).

    Google Scholar 

  3. Babin A.V. and Vishik M.I. Unstable invariant sets of semigroups of non-linear operators and their perturbations.-Usp. Matem. Nauk 1986, v. 41, No. 4 (in Russian).

    Google Scholar 

  4. Zvyagin V.G. The theory of Fredholm mappings and non-linear boundary-value problems.-A methodical elaboration, Voronezh, 1983 (in Russian).

    Google Scholar 

  5. Zvyagin V.G. Diffeomorphisms of Banach spaces generated by the Dirichlet problem for elliptic equations. Workshop on the theory of operators in functional spaces (Abstracts). Minsk, 1982 (in Russian).

    Google Scholar 

  6. Zvyagin V.G. On the theory of generally condensing perturbations of continuous mappings.-Topological and geometrical methods in mathematical physics. Voronezh, 1983 (in Russian).

    Google Scholar 

  7. Borisovich A.Yu. and Zvyagin V.G. On global invertibility of non-linear operators generated by boundary-value problems.-Approximate methods of studying differential equations and their applications. Kuibyshev, 1983 (in Russian).

    Google Scholar 

  8. Zvyagin V.G. and Morgunov A.F. Diffeomorphisms of Banach spaces generated by an initial-boundary-value problem for parabolic equations.-Deposited at VINITI, 1986, No. 6536-B86 (in Russian).

    Google Scholar 

  9. Elworthy K.D. and Tromba A.J. Degree theory on Banach manifolds.-Proc. Sympos. Pure Math. 1970, v. 18.

    Google Scholar 

  10. Pokhozhaev S.I. On non-linear operators having a weakly closed range and on quasilinear elliptic equations.-Matem. Sbornik 1969, No. 78 (in Russian).

    Google Scholar 

  11. Babin A.V. Finite-dimensional character of the kernel and cokernel of elliptic quasilinear mappings.-Matem. Sbornik 1974, No. 3 (in Russian).

    Google Scholar 

  12. Smale S. An infinite-dimensional version of Sard's theorem.-Amer. J. Math. 1965, v. 87.

    Google Scholar 

  13. Schechter M. Various Types of Boundary Conditions for Elliptic Equations.-Commun. on Pure and Applied Math. 1960, v. 13, No.3.

    Google Scholar 

  14. Hörmander L. Linear partial differential operators.-Springer-Verlag, Berlin, 1963.

    CrossRef  MATH  Google Scholar 

  15. Saut J.C. and Temam R. Generic properties of non-linear boundary-value problems.-Commun. Partial Diff. Equations, 1979, No.4(3).

    Google Scholar 

  16. Skrypnik I.V. Topological methods of studying general non-linear elliptic boundary-value problems.-Geometry and topology in global non-linear problems. Voronezh, 1984 (in Russian).

    Google Scholar 

  17. Ladyzhenskaya O.A., Solonnikov V.A., and Uraltseva N.N. Linear and quasilinear equations of parabolic type.-Moscow, 1967 (in Russian).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1990 Springer-Verlag

About this chapter

Cite this chapter

Zvyagin, V.G. (1990). The properness of elliptic and parabolic differential operators. In: Borisovich, Y.G., Gliklikh, Y.E., Vershik, A.M. (eds) Global Analysis - Studies and Applications IV. Lecture Notes in Mathematics, vol 1453. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0085952

Download citation

  • DOI: https://doi.org/10.1007/BFb0085952

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-53407-5

  • Online ISBN: 978-3-540-46861-5

  • eBook Packages: Springer Book Archive