A boundary value problem for Poisson's two-media equation in L-p(2)-spaces

In the paper we study a binding boundary value problem for two media for Poisson's equation mu Delta mu = f(x) with solutions in the class L-p(2)(R-+/-(3)), 1 < p < infinity, with the corresponding seminorm, where [GRAPHICS] It is proved that the solution exists for all f(x) is an element of L-p, and a priori estimates of the solution are obtained with the help of multiplicators in the space L-p(2)(B-+/-(3)). An explicit solution of the problem for all f(x) is an element of (C) over circle is obtained. The kernel of the operator generated by the problem is constructed (in explicit form) as a polynomial of the first degree.