Dirichlet problem for degenerate Hessian quotient type curvature equations

2024/05/06 by Chen, Xiaojuan, Tu, Qiang, Xiang, Ni · 1 citation
#35J15 #35J70 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2405.03422

Abstract

In the paper, we prove the existence and uniqueness results of the C^1,1 regular graphic hypersurface for Dirichlet problem of a class of degenerate Hessian quotient type curvature equations under the condition ψ^(1)/(k-l)∈ C^1,1(Ω×ℝ×\mathbbSⁿ). Specially, we also consider the second order derivative estimates for the corresponding degenerate Hessian type curvature equations under the optimal condition ψ^(1)/(k-1)∈ C^1,1(Ω×ℝ×\mathbbSⁿ).

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• The Dirichlet problem for Hessian quotient type curvature equations in Minkowski space

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