Том 71
№ 6

All Issues

Kirichenko E. V.

Articles: 1
Article (Russian)

On the dirichlet problem for an improperly elliptic equation

Burskii V. P., Kirichenko E. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2011. - 63, № 2. - pp. 156-164

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.