Pogorelov estimates for semi-convex solutions of 𝑘-curvature equations

IF 0.8 3区数学 Q2 MATHEMATICS

Proceedings of the American Mathematical Society Pub Date : 2024-03-09 DOI:10.1090/proc/16820

Xiaojuan Chen, Qiang Tu, Ni Xiang

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引用次数: 0

Abstract

In this paper, we consider k k -curvature equations σ k ( κ [ M u ] ) = f ( x , u , ∇ u ) \sigma _k(\kappa [M_u])=f(x,u,\nabla u) subject to ( k + 1 ) (k+1) -convex Dirichlet boundary data instead of affine Dirichlet data of Sheng, Urbas, and Wang [Duke Math. J. 123 (2004), pp. 235–264]. By using the crucial concavity inequality for Hessian operator of Lu [Calc. Var. Partial Differential Equations 62 (2023), p.23], we derive Pogorelov estimates of semi-convex admissible solutions for these k k -curvature equations.

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𝑘曲率方程半凸解的波格雷洛夫估计值

本文考虑 k k -曲率方程 σ k ( κ [ M u ] ) = f ( x , u ,∇ u ) \sigma _k(\kappa [M_u])=f(x,u,\nabla u) subject to ( k + 1 ) (k+1) -convex Dirichlet boundary data instead of affine Dirichlet data of Sheng, Urbas, and Wang [Duke Math. J 123 (2004)].123 (2004), pp.］通过使用 Lu [Calc. Var. Partial Differential Equations 62 (2023), p.23] 的 Hessian 算子的关键凹不等式，我们推导出了这些 k k -曲率方程的半凸可纳解的 Pogorelov 估计值。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Proceedings of the American Mathematical Society 数学-数学

CiteScore

1.70

自引率

10.00%

发文量

207

审稿时长

2-4 weeks

期刊介绍： All articles submitted to this journal are peer-reviewed. The AMS has a single blind peer-review process in which the reviewers know who the authors of the manuscript are, but the authors do not have access to the information on who the peer reviewers are. This journal is devoted to shorter research articles (not to exceed 15 printed pages) in all areas of pure and applied mathematics. To be published in the Proceedings, a paper must be correct, new, and significant. Further, it must be well written and of interest to a substantial number of mathematicians. Piecemeal results, such as an inconclusive step toward an unproved major theorem or a minor variation on a known result, are in general not acceptable for publication. Longer papers may be submitted to the Transactions of the American Mathematical Society. Published pages are the same size as those generated in the style files provided for AMS-LaTeX.