On Dirichlet problem for string equation, Poncelet problem, Pell-Abel equation, and some other related problems

  • V. P. Burskii
  • A. S. Zhedanov

Abstract

In a plane domain bounded by a biquadratic curve, we consider the problem of the uniqueness of a solution of the Dirichlet problem for the string equation. We show that this problem is equivalent to the classical Poncelet problem in projective geometry for two appropriate ellipses and also to the problem of the solvability of the Pell-Abel algebraic equation; some other related problems are also considered.
Published
25.04.2006
How to Cite
Burskii, V. P., and A. S. Zhedanov. “On Dirichlet Problem for String Equation, Poncelet Problem, Pell-Abel Equation, and Some Other Related Problems”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, no. 4, Apr. 2006, pp. 435–450, https://umj.imath.kiev.ua/index.php/umj/article/view/3466.
Section
Research articles