Spectral asymptotic and positivity for singular Dirichlet-to-Neumann\n operators

2020/05/11 by Ali BenAmor, BenAmor, Ali
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical methods in inverse problems #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2005.05059

openalex publication_date 2020/05/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In the framework of Hilbert spaces we shall give necessary and sufficient\nconditions to define a Dirichlet-to-Neumann operator via Dirichlet principle.\nFor singular Dirichlet-to-Neumann operators we will establish Laurent expansion\nnear singularities as well as Mittag--Leffler expansion for the related\nquadratic form. The established results will be exploited to solve definitively\nthe problem of positivity of the related semigroup in the L² setting. The\nobtained results are supported by some examples on Lipschitz domains. Among\nother results, we shall demonstrate that regularity of the boundary may affect\npositivity and derive Mittag-Leffler expansion for the eigenvalues of singular\nDirichlet-to-Neumann operators.\n

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