THE DIRICHLET PROBLEM FOR THE ELLIPTIC SYSTEM OF WEAKLY CONNECTED SECOND ORDER DIFFERENTIAL EQUATIONS WITH DISCONTINUOUS BOUNDARY CONDITIONS

Abstract

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 $M_D(х_1,х_2,\ldots,х_h,\infty; l_1,l_2,\ldots,l_h,l_{h+1})$ class is observed $$\begin{cases} A\dfrac{\partial^2u}{\partial x^2} +2B\dfrac{\partial^2u}{\partial x\partial y}+C\dfrac{\partial^2u}{\partial y^2}=0,\\ u(x,0)=f(x), x\neq х_1,х_2,\ldots,х_h, \end{cases}$$ the boundary problem, where $f(x)\in N_\Gamma (х_1,х_2,\ldots,х_h,\infty; l_1,l_2,\ldots,l_h,l_{h+1})$ . It is proved that the problem has a solution and one solution is found.