Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

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Bull. Korean Math. Soc. 2024; 61(2): 355-379

Online first article January 23, 2024      Printed March 31, 2024

https://doi.org/10.4134/BKMS.b230117

Copyright © The Korean Mathematical Society.

Curvature estimates for a class of fully nonlinear elliptic equations with general right hand sides

Jundong Zhou

Fuyang Normal University

Abstract

In this paper, we establish the curvature estimates for a class of curvature equations with general right hand sides depending on the gradient. We show an existence result by using the continuity method based on a priori estimates. We also derive interior curvature bounds for solutions of a class of curvature equations subject to affine Dirichlet data.

Keywords: Curvature estimates, hypersurfaces, continuity method, interior curvature bounds

MSC numbers: 53C42, 35J60

Supported by: This work was supported by the Natural Science Foundation of Anhui Province Education Department(KJ2021A0659, KJ2021A0661, 2022AH051320 and 2022AH051322), University Excellent Young Talents Research Project of Anhui Province (gxyq2022039), Scientific Research Foundation of Fuyang Normal University(2021KYQD0011).