Skip to main content
SpringerLink
Log in

Boundary-value problems for the wave equation with Lévy Laplacian in the Gâteaux class

  • Published:
Ukrainian Mathematical Journal Aims and scope

We present the solutions of the initial-value problem in the entire space and the solutions of the boundary-value and initial-boundary-value problems for the wave equation

$$ \frac{{{\partial^2}U\left( {t,x} \right)}}{{\partial {x^2}}} = {\Delta_L}U\left( {t,x} \right) $$

with infinite-dimensional Lévy Laplacian Δ L in the class of Gâteaux functions.

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

References

  1. P. Lévy, Problémes Concrets d’Analyse Foncionnelle, Gauthier-Villars, Paris (1951).

    Google Scholar 

  2. M. N. Feller, The Lévy Laplacian, Cambridge Univ. Press, Cambridge, etc. (2005).

    Book  MATH  Google Scholar 

  3. G. E. Shilov, “Some problems of analysis in Hilbert spaces. I,” Funkts. Anal. Prilozh., 1, No. 2, 81–90 (1967).

    Google Scholar 

Download references

Author information

Authors and Affiliations

    Consortia

    M. N. Feller

    Additional information

    Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 61, No. 11, pp. 1564–1574, November, 2009.

    Rights and permissions

    Reprints and permissions

    About this article

    Cite this article

    M. N. Feller. Boundary-value problems for the wave equation with Lévy Laplacian in the Gâteaux class. Ukr Math J 61, 1839–1852 (2009). https://doi.org/10.1007/s11253-010-0316-8

    Download citation

    • Received:

    • Published:

    • Issue Date:

    • DOI: https://doi.org/10.1007/s11253-010-0316-8

    Search

    Navigation