Second order estimates for convex solutions of degenerate k-Hessian equations

Heming Jiao; Zhizhang Wang

doi:10.1016/j.jfa.2023.110248

Second order estimates for convex solutions of degenerate k-Hessian equations

Heming Jiao^*
, Zhizhang Wang

^*Corresponding author for this work

School of Mathematics, Harbin Institute of Technology
Fudan University

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

6 Scopus citations

Abstract

The C^1,1 estimate of the Dirichlet problem for degenerate k-Hessian equations with non-homogenous boundary conditions is an open problem, if the right hand side function f is only assumed to satisfy f^1/(k−1)∈C^1,1. In this paper, we solve this problem for convex solutions defined in the strictly convex bounded domain.

Original language	English
Article number	110248
Journal	Journal of Functional Analysis
Volume	286
Issue number	3
DOIs	https://doi.org/10.1016/j.jfa.2023.110248
State	Published - 1 Feb 2024
Externally published	Yes

Keywords

Convex solutions
Degenerate k-Hessian equations
Second order estimates

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10.1016/j.jfa.2023.110248

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title = "Second order estimates for convex solutions of degenerate k-Hessian equations",

abstract = "The C1,1 estimate of the Dirichlet problem for degenerate k-Hessian equations with non-homogenous boundary conditions is an open problem, if the right hand side function f is only assumed to satisfy f1/(k−1)∈C1,1. In this paper, we solve this problem for convex solutions defined in the strictly convex bounded domain.",

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AU - Jiao, Heming

AU - Wang, Zhizhang

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N2 - The C1,1 estimate of the Dirichlet problem for degenerate k-Hessian equations with non-homogenous boundary conditions is an open problem, if the right hand side function f is only assumed to satisfy f1/(k−1)∈C1,1. In this paper, we solve this problem for convex solutions defined in the strictly convex bounded domain.

AB - The C1,1 estimate of the Dirichlet problem for degenerate k-Hessian equations with non-homogenous boundary conditions is an open problem, if the right hand side function f is only assumed to satisfy f1/(k−1)∈C1,1. In this paper, we solve this problem for convex solutions defined in the strictly convex bounded domain.

KW - Convex solutions

KW - Degenerate k-Hessian equations

KW - Second order estimates

UR - https://www.scopus.com/pages/publications/85178295341

U2 - 10.1016/j.jfa.2023.110248

DO - 10.1016/j.jfa.2023.110248

M3 - 文章

AN - SCOPUS:85178295341

SN - 0022-1236

VL - 286

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 3

M1 - 110248

ER -

Second order estimates for convex solutions of degenerate k-Hessian equations

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Keywords

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