### Abstract

Consider two perfectly conducting spheres in a homogeneous medium where the current-electric field relation is the power law. Electric field E blows up in the L∞-norm as δ, 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 δ. If the current-electric field relation is linear, see similar results obtained earlier in [E. S. Bao, Y. Y. Li, and B. Yin, Arch. Ration. Mech. Anal., 193 (2009), pp. 195-226; H. Kang, M. Lim, and K. H. Yun, preprint, http://arxiv.org/abs/1105.4328v1, 2011; M. Lim and K. Yun, Comm. Partial Differential Equations, 34 (2009), pp. 1287-1315; K. Yun, SIAM J. Appl. Math., 67 (2007), pp. 714-730; K. Yun, J. Math. Anal. Appl., 350 (2009), pp. 306-312].

Original language | English (US) |
---|---|

Pages (from-to) | 727-743 |

Number of pages | 17 |

Journal | Multiscale Modeling and Simulation |

Volume | 10 |

Issue number | 3 |

DOIs | |

State | Published - Oct 8 2012 |

### All Science Journal Classification (ASJC) codes

- Chemistry(all)
- Modeling and Simulation
- Ecological Modeling
- Physics and Astronomy(all)
- Computer Science Applications

## Fingerprint Dive into the research topics of 'Blow-up of solutions to a p-laplace equation'. Together they form a unique fingerprint.

## Cite this

*Multiscale Modeling and Simulation*,

*10*(3), 727-743. https://doi.org/10.1137/110857167