Blow-up of solutions to a p-Laplace equation

TL;DR

This paper rigorously analyzes the rate at which the electric field becomes unbounded as two conducting spheres in a homogeneous medium approach each other, providing a mathematical justification for the blow-up behavior.

Contribution

It offers a concise, rigorous derivation of the blow-up rate of the electric field in a p-Laplace equation model with conducting spheres.

Findings

Electric field blows up as spheres approach each other

Derived explicit rate of blow-up in terms of distance

Provides mathematical justification for observed phenomena

Abstract

Consider two perfectly conducting spheres in a homogeneous medium where the current-electric field relation is the power law. Electric field blows up in the L-infinity norm as the distance between the conductors tends to zero. We give here a concise rigorous justification of the rate of this blow-up in terms of the distance between the conductors.