Multidimensional diffusial processes with partially reflective screen on hyperplane (in Ukrainian)

At the domain $D_i = \{x: x=(x_1, \dots, x_m) \in \mathbb{R}^m, (-1)^i x_1 > 0 \}$, $i=1,2,$ finite-dimensional Euclidean space $\mathbb{R}^m$, $m \ge 2,$ there is given diffusion process controlled by an elliptic operator $$L_i = \frac{1}{2} \sum_{k,j=1}^m b_{kj}^{(i)} \frac{\partial^2}{\partial x_k \partial x_j},$$ where the matrix $B_i = (b_{kj}^{(i)})$ is constant, symmetrixc and positive definite. We consider a problem of describing a certain class of continuous Feller processes in $\mathbb{R}^m$, which coincide with the given diffusion processes in the domains $D_1$ and $D_2$. To solve it, we will use methods from the theory of parabolic equations with discontinuous coefficients. Note that the case where $B_1=B_2=B$ and $B^{-1}$ is a sufficiently regular matrix was early considered by Portenko. The one-dimensional case was also studied by Lager and Schenk.