Jordan chains of elliptic partial differential operators and Dirichlet-to-Neumann maps

2019/05/28 by Jussi Behrndt, Behrndt, J., A. F. M. ter Elst +1
Computer Science · Mathematics · #35J57 #35P05 #47A75 #47F05 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical methods in inverse problems #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1905.12041

openalex publication_date 2019/05/28 · openalex created_date 2019/06/07 · openalex updated_date 2026/07/28

Abstract

Let Ω⊂ \bf R^d be a bounded open set with Lipschitz boundary Γ. It will be shown that the Jordan chains of m-sectorial second-order elliptic partial differential operators with measurable coefficients and (local or non-local) Robin boundary conditions in L₂(Ω) can be characterized with the help of Jordan chains of the Dirichlet-to-Neumann map and the boundary operator from H^1/2(Γ) into H^-1/2(Γ). This result extends the Birman--Schwinger principle in the framework of elliptic operators for the characterization of eigenvalues, eigenfunctions and geometric eigenspaces to the complete set of all generalized eigenfunctions and algebraic eigenspaces.

Citations

• Characterizations of generalized poles by pole cancellation functions of higher order

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