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

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:503

Article

BenAmor, Ali¹ 

[1] Univ Sousse, High Sch Transport & Logist, 4023 Cite Erriadh, Sousse, Tunisia

关键词: Dirichlet-to-Neumann operator;    Spectral asymptotic;    Positivity preserving;    Mittag-Leffler expansion;   

DOI  :  10.1016/j.jmaa.2021.125073

来源: Elsevier

【 摘 要 】

In the framework of Hilbert spaces we shall give necessary and sufficient conditions to define a Dirichlet-to-Neumann operator via Dirichlet principle. Analyzing singular Dirichlet-to-Neumann operators, we will establish Laurent expansion near singularities as well as Mittag-Leffler expansion for the related quadratic forms. The established results will be exploited to solve definitively the problem of positivity of the related semigroup in the framework of Lebesgue spaces. The obtained results are supported by some examples where we analyze properties of singular Dirichlet-toNeumann operators related to Neumann and Robin Laplacian on Lipschitz domains. Among other results, we shall demonstrate that regularity of the boundary may affect positivity and derive Mittag-Leffler expansion for the eigenvalues of singular Dirichlet-to-Neumann operators. (c) 2021 Published by Elsevier Inc.

【 授权许可】

Free