We study an elliptic transmission problem in Banach spaces. The problem is considered on the juxtaposition of two intervals, one of which of small length δ, and models physical phenomena in media constituted by two parts with different physical characteristics. We obtain results of existence, uniqueness, maximal regularity and optimal dependence on the parameter δ for Lp solutions of the problem. The main tools of our approach are impedance and admittance operators (i.e. Dirichlet-to-Neumann and Neumann-to-Dirichlet operators) and H∞ functional calculus for sectorial operators in Banach spaces.

An abstract transmission problem in a thin layer, I: Sharp estimates

DORE, GIOVANNI;FAVINI, ANGELO;
2011

Abstract

We study an elliptic transmission problem in Banach spaces. The problem is considered on the juxtaposition of two intervals, one of which of small length δ, and models physical phenomena in media constituted by two parts with different physical characteristics. We obtain results of existence, uniqueness, maximal regularity and optimal dependence on the parameter δ for Lp solutions of the problem. The main tools of our approach are impedance and admittance operators (i.e. Dirichlet-to-Neumann and Neumann-to-Dirichlet operators) and H∞ functional calculus for sectorial operators in Banach spaces.
G.Dore; A. Favini; R. Labbas; K. Lemrabet
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11585/104102
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