Dirichlet-to-Neumann semigroup with respect to a general second order\n eigenvalue problem

2016/06/13 by Jamil Abreu, Abreu, Jamil, Érika Capelato +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1606.03961

openalex publication_date 2016/06/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we present a preliminary study on the Dirichlet-to-Neumann\noperator with respect to a second order elliptic operator with measurable\ncoefficients, including first order terms, namely, the operator on\nL²(\∂\Ω) given by \φ\↦ \∂_\νu where u is a\nweak solution of \
left

beginaligned -
rm div
, (a
nablaν) +b
cdot
nabla u -
rm div
, (cu)+du amp; =
lambda u


texton

Omega,

ν|
_{partial
Omega} amp; =
varphi .
endaligned
right. Under\nsuitable assumptions on the matrix-valued function a, on the vector fields\nb and c, and on the function d, we investigate positivity,\nsub-Markovianity, irreducibility and domination properties of the associated\nsemigroups.\n

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