Skip to main content
SpringerLink
Log in

On a class of sectorial functional-differential operators

  • Partial Differential Equations
  • Published:
Differential Equations Aims and scope Submit manuscript

Abstract

In a bounded domain containing the origin, we consider a partial differential equation whose leading terms contain transformations of arguments of the unknown function in the form of contractions and dilations. We study algebraic conditions under which the operator occurring in the equation satisfies the Gårding inequality. A criterion obtained earlier for constant coefficients cannot be generalized to the case of variable coefficients. We suggest a new approach to the solution of the problem in the case of variable coefficients based on the pseudodifferential operator calculus.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Kato, T., Perturbation Theory for Linear Operators, Heidelberg: Springer, 1966. Translated under the title Teoriya vozmushcheniya lineinykh operatorov, Moscow: Mir, 1972.

    MATH  Google Scholar 

  2. Shamin, R.V., On Spaces of Initial Data for Differential Equations in Hilbert Space, Mat. Sb., 2003, vol. 194, no. 9, pp. 1411–1426.

    Article  MathSciNet  MATH  Google Scholar 

  3. Kato, T., Fractional Powers of Dissipative Operators, J. Math. Soc. Japan, 1961, vol. 13, pp. 246–274.

    Article  MathSciNet  MATH  Google Scholar 

  4. Skubachevskii, A.L. and Shamin, R.V., The Mixed Boundary Value Problem for Parabolic Differential-Difference Equation, Funct. Differ. Equ., 2001, vol. 8, pp. 407–424.

    MathSciNet  MATH  Google Scholar 

  5. Vishik, M.I., On Strongly Elliptic Systems of Differential Equations, Mat. Sb., 1951, vol. 29, no. 3, pp. 615–676.

    MathSciNet  Google Scholar 

  6. Gårding, L., Dirichlet’s Problem for Linear Elliptic Partial Differential Equations, Math. Scand., 1953, vol. 1, pp. 55–72.

    MathSciNet  MATH  Google Scholar 

  7. Skubachevskii, A.L., The First Boundary Value Problem for Strongly Elliptic Differential-Difference Equations, J. Differential Equations, 1986, vol. 63, pp. 332–361.

    Article  MathSciNet  Google Scholar 

  8. Rossovskii, L.E., Coercivity of Functional-Differential Equations, Mat. Zametki, 1996, vol. 59, pp. 103–113.

    MathSciNet  Google Scholar 

  9. Agranovich, M.S. and Vishik, M.I., Elliptic Problems with Parameter, and Parabolic Problems of General Form, Uspekhi Mat. Nauk, 1964, vol. 19, no. 3, pp. 53–161.

    MATH  Google Scholar 

  10. Taylor, M., Psevdodifferentsial’nye operatory (Pseudodifferential Operators), Moscow, 1985.

  11. Hörmander, L., The Analysis of Linear Differential Operators, Heidelberg, Springer Verlag, 1983. Translated under the title Analiz lineinykh differentsial’nykh operatorov s chastnymi proizvodnymi, Moscow: Mir, 1987, vol. 3.

    Book  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Peoples’ Friendship University of Russia, Moscow, Russia

    L. E. Rossovskii

Authors
  1. L. E. Rossovskii
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Original Russian Text © L.E. Rossovskii, 2012, published in Differentsial’nye Uravneniya, 2012, Vol. 48, No. 2, pp. 227–237.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Rossovskii, L.E. On a class of sectorial functional-differential operators. Diff Equat 48, 234–245 (2012). https://doi.org/10.1134/S0012266112020073

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0012266112020073

Keywords

Search

Navigation