We consider the transmission problem for the Laplace operator in a straight cylinder with data in . Applying the theory of the sums of operators in Banach spaces, we prove that the solution admits a decomposition into a regular part in and an explicit singular part.
In this paper we consider an abstract elliptic differential problem where the equation and the boundary conditions may contain a spectral parameter. We first prove that this problem generates an isomorphism between appropriate spaces and we establish a more precise estimate called coerciveness estimate with defect. The results obtained are applied to study some classes of elliptic, and also possibly degenerate, problems.
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