Communications in Analysis and Geometry

Volume 31 (2023)

Number 1

Motion of level sets by inverse anisotropic mean curvature

Pages: 97 – 118

DOI: https://dx.doi.org/10.4310/CAG.2023.v31.n1.a4

Authors

Francesco Della Pietra (Dipartimento di Matematica e Applicazioni, Università degli Studi di Napoli Federico II, Napoli, Italy)

Nunzia Gavitone (Dipartimento di Matematica e Applicazioni, Università degli Studi di Napoli Federico II, Napoli, Italy)

Chao Xia (School of Mathematical Sciences, Xiamen University, Xiamen, China)

Abstract

In this paper we consider the weak formulation of the inverse anisotropic mean curvature flow, in the spirit of Huisken–Ilmanen [$\href{ https://dx.doi.org/10.4310/jdg/1090349447}{15}$]. By using approximation method involving Finsler‑$p$-Laplacian, we prove the existence and uniqueness of weak solutions.

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Chao Xia is supported by the NSFC (Grant No. 11871406), by the Natural Science Foundation of Fujian Province of China (Grant No. 2017J06003), and by the Fundamental Research Funds for the Central Universities (Grant No. 20720180009).

Received 18 April 2018

Accepted 16 August 2020

Published 21 September 2023