## Abstract

Given an ∞-harmonic function (Formula presented.) on a domain (Formula presented.) consider the function (Formula presented.) If (Formula presented.) with (Formula presented.) and (Formula presented.) then it is easy to check that the streamlines of (Formula presented.) are the level sets of w and w solves the level set formulation of the inverse mean curvature flow. For less regular solutions, neither statement is true in general, but even so, w is still a weak solution of the inverse mean curvature flow under far weaker assumptions. This is proved through an approximation of (Formula presented.) by p-harmonic functions, the use of conjugate (Formula presented.) -harmonic functions, and the known connection of the latter with the inverse mean curvature flow. A statement about the regularity of (Formula presented.) arises as a by-product.

Original language | English |
---|---|

Pages (from-to) | 2124-2145 |

Journal | Communications in Partial Differential Equations |

Volume | 47 |

Issue number | 11 |

Early online date | 23 Aug 2022 |

DOIs | |

Publication status | Published - 28 Dec 2022 |

### Bibliographical note

No funding acknowledged.## Keywords

- infinity-harmonic functions
- inverse mean curvature flow
- viscosity solution
- weak solution

## ASJC Scopus subject areas

- Analysis
- Applied Mathematics