On the dirichlet problem for an improperly elliptic equation

  • V. P. Burskii
  • E. V. Kirichenko


The solvability of the inhomogeneous Dirichlet problem in a bounded domain for scalar improperly elliptic differential equation with complex coefficients is investigated. We study a model case where the unit disk is chosen as a domain and the equation does not contain lowest terms. We prove that the problem has a unique solution in the Sobolev space for special classes of Dirichlet data that are spaces of functions with exponential decrease of the Fourier coefficients.
How to Cite
Burskii, V. P., and E. V. Kirichenko. “On the Dirichlet Problem for an Improperly Elliptic Equation”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 63, no. 2, Feb. 2011, pp. 156-64, https://umj.imath.kiev.ua/index.php/umj/article/view/2707.
Research articles