M-dissipative boundary conditions and boundary tuples for Maxwell operators
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Publication:6379839
DOI10.1016/J.JDE.2022.04.006arXiv2110.04586MaRDI QIDQ6379839
I. M. Karabash, Matthias Eller
Publication date: 9 October 2021
Abstract: For Maxwell operators in Lipschitz domains, we describe all m-dissipative boundary conditions and apply this result to generalized impedance and Leontovich boundary conditions including the cases of singular, degenerate, and randomized impedance coefficients. To this end we construct Riesz bases in the trace spaces associated with the curl-operator and introduce a modified version of boundary triple adapted for the specifics of Maxwell equations, namely, to the mixed-order duality of the related trace spaces. This provides a translation of the problem to operator-theoretic settings of abstract Maxwell operators. In particular, we show that Calkin reduction operators are naturally connected with Leontovich boundary conditions and provide an abstract version of impedance boundary condition applicable to other types of wave equations. Taking Friedrichs and Krein-von Neumann extensions of related boundary operators, it is possible to associate m-dissipative Maxwell operators to arbitrary non-negative measurable impedance coefficients.
Partial differential equations of mathematical physics and other areas of application (35Qxx) Special classes of linear operators (47Bxx) General theory of linear operators (47Axx)
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