Abstract
The transmission problem for the Stokes system is studied: ∆v± = Δp±, v± = 0 in G±, v+ - v- = g, a+T(v+, p+)n - a-T(v-, p-)n = f on ∂G+. Here G+ Δc R3 is a bounded open set with Lipschitz boundary and G- is the corresponding complementary open set. Using the integral equation method we study the problem in homogeneous Sobolev spaces. Under assumption that ∂G+ is of class C1 we study this problem also in Besov spaces and Lq-solutions of the problem. We show the unique solvability of the problem. Moreover, we solve the corresponding boundary integral equations by the successive approximation method.
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