Results 21 to 30 of about 156 (134)

Generalized Liouville theorem for viscosity solutions to a singular Monge-Ampère equation

Advances in Nonlinear Analysis, 2023
In this article, we study the asymptotic behaviour at infinity for viscosity solutions to a singular Monge-Ampère equation in half space from affine geometry.
Jian Huaiyu, Wang Xianduo
doaj   +1 more source

Lp‐Curvature Measures and Lp,q‐Mixed Volumes

Journal of Function Spaces, Volume 2022, Issue 1, 2022., 2022
Motivated by Lutwak et al.’s Lp‐dual curvature measures, we introduce the concept of Lp‐curvature measures. This new Lp‐curvature measure is an extension of the classical surface area measure, Lp‐surface area measure, and curvature measure. In this paper, we first prove some properties of the Lp‐curvature measure.
Tongyi Ma, Raúl E. Curto
wiley   +1 more source

The Initial and Neumann Boundary Value Problem for a Class Parabolic Monge-Ampère Equation

Abstract and Applied Analysis, 2013
We consider the existence, uniqueness, and asymptotic behavior of a classical solution to the initial and Neumann boundary value problem for a class nonlinear parabolic equation of Monge-Ampère type. We show that such solution exists for all times and is
Juan Wang, Jinlin Yang, Xinzhi Liu
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Refined Boundary Behavior of the Unique Convex Solution to a Singular Dirichlet Problem for the Monge–Ampère Equation

Advanced Nonlinear Studies, 2018
This paper is concerned with the boundary behavior of the unique convex solution to a singular Dirichlet problem for the Monge–Ampère ...
Zhang Zhijun
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On Neumann problem for the degenerate Monge–Ampère type equations

Boundary Value Problems, 2021
In this paper, we study the global C 1 , 1 $C^{1, 1}$ regularity for viscosity solution of the degenerate Monge–Ampère type equation det [ D 2 u − A ( x , D u ) ] = B ( x , u , D u ) $\det [D^{2}u-A(x, Du)]=B(x, u, Du)$ with the Neumann boundary value ...
Juhua Shi, Feida Jiang
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Continuous and Lp estimates for the complex Monge-Ampère equation on bounded domains in ℂn

International Journal of Mathematics and Mathematical Sciences, 2002
Continuous solutions with continuous data and Lp solutions with Lp data are obtained for the complex Monge-Ampère equation on bounded domains, without requiring any smoothness of the domains.
Patrick W. Darko
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Application of isotropic geometry to the solution of the Monge–Ampere equation

Қарағанды университетінің хабаршысы. Математика сериясы
This paper explores the Monge–Ampere equation in the context of isotropic geometry. The study begins with an overview of the fundamental properties of isotropic space, including its scalar product, distance formula, and the nature of surfaces and ...
Sh.Sh. Ismoilov
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A curvature flow to the Lp Minkowski-type problem of q-capacity

Advanced Nonlinear Studies, 2023
This article concerns the Lp{L}_{p} Minkowski problem for q-capacity.
Liu Xinying, Sheng Weimin
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Simplified Geometric Approach to Freeform Beam Shaper Design

International Journal of Optics, 2020
Beam of light shaping process can be considered ultimate, if both irradiance and wavefront spatial distributions are under control and both can be shaped arbitrarily.
Jacek Wojtanowski, Tadeusz Drozd
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On an {\it a priori} $L^\infty$ estimate for a class of Monge-Ampère type equations on compact almost Hermitian manifolds

Cubo, 2022
We investigate Monge-Amp\`ere type equations on almost Hermitian manifolds and show an \textit{a priori} $L^\infty$ estimate for a smooth solution of these equations.
Masaya Kawamura
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