发表机构
Center for Mathematics and Interdisciplinary Sciences, Fudan University; Shanghai Institute for Mathematics and Interdisciplinary Sciences (SIMIS); School of Mathematics and Shing-Tung Yau Center of Southeast University, Southeast University（复旦大学数学与交叉科学研究院; 上海数学与交叉学科研究院; 东南大学数学学院及苏步青应用数学中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对有界区域上n-1型增广Hessian方程的斜边值问题，在无凸性条件下建立经典椭圆解的全局存在唯一性理论，涵盖多个相关领域的方程应用。
AI 中文摘要
本文研究有界区域上n-1型增广Hessian方程的斜边值问题的全局正则性，未对区域或n-1型增广Hessian方程中的矩阵值函数施加任何凸性条件。我们通过推导直至二阶导数的全局先验估计，建立了经典椭圆解的全局存在性与唯一性理论。除了n-1型Monge-Ampère算子在最优运输和几何光学中的已知应用外，该一般理论还包含Li-Sheng（2011年，《Pac. J. Math.》第251卷，第337-359页）提出的方程，以及Guan-Qiu-Yuan（2019年，《Adv. Math.》第343卷，第538-566页）提出的与Chern-Ricci形式共形形变相关的完全非线性椭圆方程。
英文摘要
In this paper, we study the global regularity of oblique boundary value problems for n-1 type augmented Hessian equations on a bounded domain, without imposing any convexity condition either on the domain or on the matrix-valued function in the n-1 type augmented Hessian equations. We establish a global existence and uniqueness theory for classical elliptic solutions by deriving global a priori estimates up to second-order derivatives. Besides the known applications for n-1 type Monge-Ampere operators in optimal transportation and geometric optics, the general theory here embraces equations raised by Li-Sheng, Some Dirichlet problems arising from conformal geometry. Pac. J. Math. 251, 2011, 337-359 and Guan-Qiu-Yuan, Fully nonlinear elliptic equations for conformal deformations of Chern-Ricci forms. Adv. Math. 343, 2019, 538-566.
CommentsOblique boundary value problems. n-1 type Augmented Hessian equations. Global second-derivative estimates. Gradient estimates. Classical solvability
