On the Dirichlet problem with an asymptotic condition for an elliptic system strongly degenerate at a point
The paper deals with a system which is elliptic (in the Petrovskii sense) in a bounded domain and strongly degenerate at the inner point \(0\) of the domain. The aim of the paper is to consider a modified Dirichlet problem in the class of vector functions that unboundedly increase (in the absolute value) as \(x\to 0\). The modification means that in addition to a Dirichlet-type condition on the boundary, the principal term of the asymptotics of a solution at the point \(0\) is given. The existence and uniqueness of a solution of the problem considered in a weighted class of Hölder vector functions is proved.
scientific article; zbMATH DE number 1912595