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Title: Optimal estimates from below for Green functions of higher order elliptic operators with variable leading coefficients
Author(s): Grunau, Hans-ChristophLook up in the Integrated Authority File of the German National Library
Issue Date: 2021
Type: Article
Language: English
URN: urn:nbn:de:gbv:ma9:1-1981185920-997772
Subjects: Almost positivity
Powers of second order operators
Dirichlet problem
Green function estimates
Abstract: Estimates from above and below by the same positive prototype function for suitably modified Green functions in bounded smooth domains under Dirichlet boundary conditions for elliptic operators L of higher order 2m ≥ 4 have been shown so far only when the principal part of L is the polyharmonic operator (−Δ)m. In the present note, it is shown that such kind of result still holds when the Laplacian is replaced by any second order uniformly elliptic operator in divergence form with smooth variable coefficients. For general higher order elliptic operators, whose principal part cannot be written as a power of second order operators, it was recently proved that such kind of result becomes false in general.
Open Access: Open access publication
License: (CC BY 4.0) Creative Commons Attribution 4.0(CC BY 4.0) Creative Commons Attribution 4.0
Sponsor/Funder: Projekt DEAL 2021
Journal Title: Archiv der Mathematik
Publisher: Springer
Publisher Place: Berlin
Volume: 117
Original Publication: 10.1007/s00013-021-01597-x
Page Start: 95
Page End: 104
Appears in Collections:Fakultät für Mathematik (OA)

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