Newtonian Potential

  • Lester L. HelmsEmail author
Part of the Universitext book series (UTX)


This chapter commences with the study of subnewtonian kernels that share many of the properties of the Newtonian kernel \(1/|x-y|^{n-2}\) on \(R^n \times R^n\) related to transforming a given function into another and the determination of properties of the transformed function passed on through the kernel. Poisson’s equation \(\triangle u = f\) is shown to be solvable if \(f\) has adequate smoothness properties. The last section introduces Schwarz’s Reflection Principle that allows the extension of function on one side of region \(\Omega \) that is symmetric relative to a hyperplane to all of \(\Omega \) with a vanishing normal derivative at points of the hyperplane that are in \(\Omega \).


Newtonian Potential Reflection Principle Fundamental Harmonic Function Regular Boundary Point Nonhomogeneous Conditions 
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Copyright information

© Springer-Verlag London 2014

Authors and Affiliations

  1. 1.University of IllinoisUrbanaUSA

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