On constructing a sticky membrane located on a given surface for a symmetric $\alpha$-stable process

For a symmetric $\alpha$-stable stochastic process with $\alpha\in(1,2)$ in a Euclidean space, a membrane located on a fixed bounded closed surface $S$ is constructed in such a way that the points of the surface possess the property of delaying the process with some given positive coefficient $(p(x))_{x\in S}$. In other words, the points of $S$ are sticky for the process constructed. We show that this process is associated with some initial-boundary value problem for pseudo-differential equations related to a symmetric $\alpha$-stable process.