Optimal global regularity for minimal graphs over convex domains in hyperbolic space

doi:10.1007/s11464-021-0963-0

Front. Math. China

2022, Vol. 17

Issue (5) : 905-914 https://doi.org/10.1007/s11464-021-0963-0

RESEARCH ARTICLE

Optimal global regularity for minimal graphs over convex domains in hyperbolic space

You LI, Yannan LIU(

)

School of Mathematics and Statistics, Beijing Technology and Business University, Beijing 100048, China

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Abstract

We use the concept of the inside-(a, η, h) domain to construct a subsolution to the Dirichlet problem for minimal graphs over convex domains in hyperbolic space. As an application, we prove that the Hölder exponent $max {1 / a, 1 / (n + 1)}$ for the problem is optimal for any $a ∈ [2, + ∞]$ .

Keywords Minimal graph equation optimal regularity global regularity

Corresponding Author(s): Yannan LIU

Issue Date: 28 December 2022

Cite this article:

You LI,Yannan LIU. Optimal global regularity for minimal graphs over convex domains in hyperbolic space[J]. Front. Math. China, 2022, 17(5): 905-914.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-021-0963-0
https://academic.hep.com.cn/fmc/EN/Y2022/V17/I5/905

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