# Approximate Green’s function for the conductivity equation with conormal coefficient

Approximate Green’s function for the conductivity equation with conormal coefficient We construct an approximate Green’s function for $$L_{\gamma }:={\nabla } \cdot \gamma (x) {\nabla } u(x)$$ L γ : = ∇ · γ ( x ) ∇ u ( x ) , which belongs to a class of Fourier integral operators (FIOs) associated to two canonical relations. This leads to analysis of the composition of two FIOs, associated to a canonical relation with a zero section problem. The resulting composition is a sum of two FIOs, each associated to two intersecting canonical relations. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Pseudo-Differential Operators and Applications Springer Journals

# Approximate Green’s function for the conductivity equation with conormal coefficient

, Volume 8 (3) – Nov 1, 2016
35 pages

/lp/springer_journal/approximate-green-s-function-for-the-conductivity-equation-with-WPdnyHT71C
Publisher
Springer International Publishing
Subject
Mathematics; Analysis; Operator Theory; Partial Differential Equations; Functional Analysis; Applications of Mathematics; Algebra
ISSN
1662-9981
eISSN
1662-999X
D.O.I.
10.1007/s11868-016-0176-6
Publisher site
See Article on Publisher Site

### Abstract

We construct an approximate Green’s function for $$L_{\gamma }:={\nabla } \cdot \gamma (x) {\nabla } u(x)$$ L γ : = ∇ · γ ( x ) ∇ u ( x ) , which belongs to a class of Fourier integral operators (FIOs) associated to two canonical relations. This leads to analysis of the composition of two FIOs, associated to a canonical relation with a zero section problem. The resulting composition is a sum of two FIOs, each associated to two intersecting canonical relations.

### Journal

Journal of Pseudo-Differential Operators and ApplicationsSpringer Journals

Published: Nov 1, 2016

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