Wolfram Library Archive

Courseware Demos MathSource Technical Notes
All Collections Articles Books Conference Proceedings

Regularization of radial solutions of p-Laplace equations, and computations using infinite series

Philip Korman
Organization: University of Cincinnati
Department: Department of Mathematical Sciences
Journal / Anthology

Electronic Journal of Qualitative Theory of Differential Equations
Year: 2015
Volume: 40
Page range: 1-8

We consider radial solutions of equations with the p-Laplace operator in Rn. We introduce a change of variables, which in effect removes the singularity at r = 0. While solutions are not of class C2, in general, we show that solutions are C2 functions of r p 2(p􀀀1) . Then we express the solution as an infinite series in powers of r p p􀀀1 , and give explicit formulas for its coefficients. We implement this algoritheorem, using Mathematica. Mathematica’s ability to perform the exact computations turns out to be crucial.

*Mathematics > Calculus and Analysis > Differential Equations