Resolution, in Lp-spaces, of transmission problems set in an unbounded domains

The goal of this work is to give a complete study of some abstract transmission problems (Pδ), for every δ > 0, set in unbounded domain composed of a half-line ]−∞, 0[ and a thin layer ]0, δ[. Existence and uniqueness results are obtained for strict solutions in UMD Banach spaces, by using essentially the semigroup theory and the Dore-Venni's Theorem given in [8].