The Dirichlet problem for the elliptic system of weakly connected second order differential equations with discontinuous boundary continuous

The Dirichlet problem is observed by different authors both for one equation and for systems of equations. In these authors’ articles the boundary function is continuous or has weak singularity (integral singularity). This article observe the case where boundary function may also have not weak singularity. In $M_D(x_1,x_2, \ldots, x_h, \infty; l_1, l_2, \ldots, l_h, l_{h+1})$ class is observed
$$A\dfrac{\partial^2 u }{\partial x^2}+2B \dfrac{\partial^2 u }{\partial x \partial y}+C \dfrac{\partial^2 u }{\partial y^2}=0,~u(x,0)=f(x),~x\neq x_1,x_2,\ldots,x_h,$$
the boundary problem, where $f(x)\in N_\Gamma(x_1,x_2,\ldots, x_h,\infty;l_1,l_2,\ldots,l_h,l_{h+1})$. It is proved that the problem has a solution and one solution is found.