Skip to main content
SpringerLink
Log in

Solution of Dirichlet's problem for the equation Δu =−1 in a convex region

  • Published:
Mathematical notes of the Academy of Sciences of the USSR Aims and scope Submit manuscript

Abstract

Let u be a solution of the following boundary-value problem: u¦Γ = 0, where Γ is a closed convex curve and Δu = −1 in the region D bounded by Γ. Then u has only one local maximum, and all its level curves are convex.

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

Literature cited

  1. M. Morse, Topological Methods in the Theory of Functions of a Complex Variable, Princeton Press, Princeton (1947).

    Google Scholar 

  2. P. S. Aleksandrov, Lectures on Analytic Geometry [in Russian], Moscow (1968).

Download references

Author information

Authors and Affiliations

  1. M. V. Lomonosov Moscow State University, USSR

    L. G. Makar-Limanov

Authors
  1. L. G. Makar-Limanov
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Matematicheskie Zametki, Vol. 9, No. 1, pp. 89–92, January, 1971.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Makar-Limanov, L.G. Solution of Dirichlet's problem for the equation Δu =−1 in a convex region. Mathematical Notes of the Academy of Sciences of the USSR 9, 52–53 (1971). https://doi.org/10.1007/BF01405053

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01405053

Keywords

Search

Navigation