The Dirichlet Problem for a Class of Prescribed Curvature Equations

Heming Jiao; Zaichen Sun

doi:10.1007/s12220-022-00994-0

The Dirichlet Problem for a Class of Prescribed Curvature Equations

Heming Jiao^*
, Zaichen Sun

^*Corresponding author for this work

School of Mathematics, Harbin Institute of Technology

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

In this paper, we consider the Dirichlet problem for a class of prescribed curvature equations. Both degenerate and non-degenerate cases are considered. The existence of the C^{1 , 1} regular graphic hypersurfaces with prescribing a class of curvatures and constant boundary is proved for the degenerate case.

Original language	English
Article number	261
Journal	Journal of Geometric Analysis
Volume	32
Issue number	11
DOIs	https://doi.org/10.1007/s12220-022-00994-0
State	Published - Nov 2022
Externally published	Yes

Keywords

C regularity
Degenerate
Prescribed curvature equations

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title = "The Dirichlet Problem for a Class of Prescribed Curvature Equations",

abstract = "In this paper, we consider the Dirichlet problem for a class of prescribed curvature equations. Both degenerate and non-degenerate cases are considered. The existence of the C1 , 1 regular graphic hypersurfaces with prescribing a class of curvatures and constant boundary is proved for the degenerate case.",

keywords = "C regularity, Degenerate, Prescribed curvature equations",

author = "Heming Jiao and Zaichen Sun",

note = "Publisher Copyright: {\textcopyright} 2022, Mathematica Josephina, Inc.",

year = "2022",

month = nov,

doi = "10.1007/s12220-022-00994-0",

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AU - Jiao, Heming

AU - Sun, Zaichen

PY - 2022/11

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N2 - In this paper, we consider the Dirichlet problem for a class of prescribed curvature equations. Both degenerate and non-degenerate cases are considered. The existence of the C1 , 1 regular graphic hypersurfaces with prescribing a class of curvatures and constant boundary is proved for the degenerate case.

AB - In this paper, we consider the Dirichlet problem for a class of prescribed curvature equations. Both degenerate and non-degenerate cases are considered. The existence of the C1 , 1 regular graphic hypersurfaces with prescribing a class of curvatures and constant boundary is proved for the degenerate case.

KW - C regularity

KW - Degenerate

KW - Prescribed curvature equations

UR - https://www.scopus.com/pages/publications/85136508613

U2 - 10.1007/s12220-022-00994-0

DO - 10.1007/s12220-022-00994-0

M3 - 文章

AN - SCOPUS:85136508613

SN - 1050-6926

VL - 32

JO - Journal of Geometric Analysis

JF - Journal of Geometric Analysis

IS - 11

M1 - 261

ER -

The Dirichlet Problem for a Class of Prescribed Curvature Equations

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Keywords

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