Abstract
We consider a class of second order strongly elliptic systems in ℝn, n ≥ 3, outside a bounded nonclosed surface S with transmission conditions on S containing a spectral parameter. Assuming that S and its boundary γ are Lipschitz, we reduce the problems to spectral equations on S for operators of potential type. We prove the invertibility of these operators in suitable Sobolev type spaces and indicate spectral consequences. Simultaneously, we prove the unique solvability of the Dirichlet and Neumann problems with boundary data on S.
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