Open Access
Translator Disclaimer
November 2020 The Dirichlet problem for a prescribed mean curvature equation
Yuki Tsukamoto
Hiroshima Math. J. 50(3): 325-337 (November 2020). DOI: 10.32917/hmj/1607396492

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.

Citation

Download Citation

Yuki Tsukamoto. "The Dirichlet problem for a prescribed mean curvature equation." Hiroshima Math. J. 50 (3) 325 - 337, November 2020. https://doi.org/10.32917/hmj/1607396492

Information

Received: 2 October 2019; Revised: 30 June 2020; Published: November 2020
First available in Project Euclid: 8 December 2020

MathSciNet: MR4184264
Digital Object Identifier: 10.32917/hmj/1607396492

Subjects:
Primary: 35J93
Secondary: 35J25

Rights: Copyright © 2020 Hiroshima University, Mathematics Program

JOURNAL ARTICLE
13 PAGES


SHARE
Vol.50 • No. 3 • November 2020
Back to Top