English

The Dirichlet problem for a prescribed mean curvature equation

Analysis of PDEs 2019-08-20 v1

Abstract

We study a prescribed mean curvature problem where we seek a surface whose mean curvature vector coincides with the normal component of a given vector field. We prove that the problem has a solution near a graphical minimal surface if the prescribed vector field is sufficiently small in a dimensionally sharp Sobolev norm.

Keywords

Cite

@article{arxiv.1908.06584,
  title  = {The Dirichlet problem for a prescribed mean curvature equation},
  author = {Yuki Tsukamoto},
  journal= {arXiv preprint arXiv:1908.06584},
  year   = {2019}
}

Comments

10 pages

R2 v1 2026-06-23T10:50:28.353Z