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We study the infinitesimal generator of the Poisson semigroup in Lp associated with homogeneous, second-order, strongly elliptic systems with constant complex coefficients in the upper-half space, which is proved to be the Dirichlet-to-Normal mapping in this setting. Also, its domain is identified as the linear subspace of the Lp-based Sobolev space of order one on the boundary of the upper-half space...
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