Open Access
2018 Fundamental matrices and Green matrices for non-homogeneous elliptic systems
Blair Davey, Jonathan Hill, Svitlana Mayboroda
Publ. Mat. 62(2): 537-614 (2018). DOI: 10.5565/PUBLMAT6221807


In this paper, we establish existence, uniqueness, and scale-invariant estimates for fundamental solutions of non-homogeneous second order elliptic systems with bounded measurable coefficients in $\mathbb{R}^n$ and for the corresponding Green functions in arbitrary open sets. We impose certain non-homogeneous versions of de Giorgi–Nash–Moser bounds on the weak solutions and investigate in detail the assumptions on the lower order terms sufficient to guarantee such conditions. Our results, in particular, establish the existence and fundamental estimates for the Green functions associated to the Schrödinger ($-\Delta+V$) and generalized Schrödinger ($-\operatorname{div} A\nabla +V$) operators with real and complex coefficients, on arbitrary domains.


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Blair Davey. Jonathan Hill. Svitlana Mayboroda. "Fundamental matrices and Green matrices for non-homogeneous elliptic systems." Publ. Mat. 62 (2) 537 - 614, 2018.


Received: 9 January 2017; Revised: 23 April 2017; Published: 2018
First available in Project Euclid: 16 June 2018

zbMATH: 06918956
MathSciNet: MR3815288
Digital Object Identifier: 10.5565/PUBLMAT6221807

Primary: 35A08 , 35B45 , 35J08 , 35J107 , 35J57

Keywords: elliptic equations , fundamental solution , Green function , ‎Schrödinger operator‎

Rights: Copyright © 2018 Universitat Autònoma de Barcelona, Departament de Matemàtiques

Vol.62 • No. 2 • 2018
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