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Function Spaces and Partial Differential EquationsVolume 1 - Classical Analysis$
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Ali Taheri

Print publication date: 2015

Print ISBN-13: 9780198733133

Published to Oxford Scholarship Online: September 2015

DOI: 10.1093/acprof:oso/9780198733133.001.0001

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Poisson Kernels and Green’s Representation Formula

Poisson Kernels and Green’s Representation Formula

(p.33) 2 Poisson Kernels and Green’s Representation Formula
Function Spaces and Partial Differential Equations

Ali Taheri

Oxford University Press

This chapter establishes Green’s representation formula and using it to arrive at Greens functions and Poisson kernels. Presenting explicit examples of Greens functions and Poisson kernels in specific geometries, e.g., an hp-ball and a half-space. It presents an introductory study of the Newtonian potential.

Keywords:   Green’s representation formula, surface potentials, Newtonian potential, Green’s functions, Poisson kernels, spherical harmonics, homogenous harmonic polynomials, addition formula

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