Эффективное решение задачи Дирихле для правильно эллиптического уравнения четвертого порядка

Abstract

We consider the Dirichlet problem for the fourth order properly elliptic equation with constant coefficients in the unit disc. We seek the solution in the class of functions which satisfy Holder condition up to the boundary with first degree derivatives. The necessary and sufficient conditions of the unique solvability of the problem are obtained. If these conditions failed, it was proved that the defect numbers of the problem are equal to one. The solution of the problem and the solvability conditions are determined in explicit form