Abstract
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 Rn 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 (-Δ+V ) and generalized Schrödinger (-divA∇+V ) operators with real and complex coefficients, on arbitrary domains.
Original language | English (US) |
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Pages (from-to) | 537-614 |
Number of pages | 78 |
Journal | Publicacions Matematiques |
Volume | 62 |
Issue number | 2 |
DOIs | |
State | Published - 2018 |
Bibliographical note
Publisher Copyright:© 2018 Universitat Autonoma de Barcelona. All rights reserved.
Keywords
- Elliptic equations
- Fundamental solution
- Green function
- Schrödinger operator