On the Dirichlet Problem with an Asymptotic Condition for an Elliptic System Strongly Degenerate at a Point

We consider a Dirichlettype problem for a system of elliptic equations of second order with a strong degeneracy at an inner point of the domain, when, in a neighborhood of this point, the principal term of the asymptotics of a solution is additionally given. We prove the existence and uniqueness of a solution of the problem considered in a weighted class of Hölder vector functions.