scholarly journals Radial solutions for fully nonlinear elliptic equations of Monge–Ampère type

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Limei Dai ◽  
Huihui Cheng ◽  
Hongfei Li
Keyword(s):  
Elliptic Equations ◽  
Nonlinear Elliptic Equations ◽  
Classical Solutions ◽  
Radial Solutions ◽  
Fully Nonlinear Elliptic Equations ◽  
Nonlinear Elliptic ◽  
Hessian Equations ◽  
Existence And Nonexistence ◽  
Moving Plane ◽  
Monge Ampere

AbstractFirst, the symmetry of classical solutions to the Monge–Ampère-type equations is obtained by the moving plane method. Then, the existence and nonexistence of radial solutions in a ball are got from the symmetry results. Finally, the existence and nonexistence of classical solutions to Hessian equations in bounded domains are considered.

Removable singularities of fully nonlinear elliptic equations

Analysis ◽  
2007 ◽  
Vol 27 (1) ◽  
Author(s):  
Friedmar Schulz
Keyword(s):  
Elliptic Equations ◽  
Nonlinear Elliptic Equations ◽  
Singular Set ◽  
Fully Nonlinear Elliptic Equations ◽  
Fully Nonlinear ◽  
Removable Singularities ◽  
Nonlinear Elliptic ◽  
Monge Ampere

In this paper we consider fully nonlinear elliptic equations of the formincluding the Monge–Ampère, the Hessian and the Weingarten equations and give conditions which ensure that a singular set

On a Class of Fully Nonlinear Elliptic Equations Containing Gradient Terms on Compact Hermitian Manifolds

2018 ◽  
Vol 70 (4) ◽  
pp. 943-960
Author(s):  
Rirong Yuan
Keyword(s):  
Elliptic Equations ◽  
A Priori ◽  
Nonlinear Elliptic Equations ◽  
Second Order ◽  
Fully Nonlinear Elliptic Equations ◽  
Fully Nonlinear ◽  
Nonlinear Elliptic ◽  
Hermitian Manifolds ◽  
Hessian Equations

AbstractIn this paper we study a class of second order fully nonlinear elliptic equations containing gradient terms on compact Hermitian manifolds and obtain a priori estimates under proper assumptions close to optimal. The analysis developed here should be useful to deal with other Hessian equations containing gradient terms in other contexts.

scholarly journals On degenerate fully nonlinear elliptic equations in balls

1987 ◽  
Vol 35 (2) ◽  
pp. 299-307 ◽  
Author(s):  
Neil S. Trudinger
Keyword(s):  
Elliptic Equations ◽  
Existence Theorems ◽  
Nonlinear Elliptic Equations ◽  
Fully Nonlinear Elliptic Equations ◽  
Neumann Problems ◽  
Nonlinear Elliptic ◽  
Degenerate Elliptic ◽  
Monge Ampere ◽  
Special Case ◽  
Nonlinear Degenerate

We establish derivative estimates and existence theorems for the Dirichlet and Neumann problems for nonlinear, degenerate elliptic equations of the form F (D2u) = g in balls. The degeneracy arises through the possible vanishing of the function g and the degenerate Monge-Ampère equation is covered as a special case.

Regularity of the Dirichlet Problem for the Non-degenerate Complex Quotient Equations

2020 ◽  
Author(s):  
Qiqi Zhang
Keyword(s):  
Dirichlet Problem ◽  
Elliptic Equations ◽  
Symmetric Functions ◽  
Hessian Matrix ◽  
Nonlinear Elliptic Equations ◽  
Fully Nonlinear Elliptic Equations ◽  
Linear Combinations ◽  
Nonlinear Elliptic ◽  
Hessian Equations ◽  
Special Cases

Abstract We study the solvability for the Dirichlet problem of a class of fully nonlinear elliptic equations over complex domains in $\textbf{C}^n$. The equations are in the form of the linear combinations of the elementary symmetric functions of the Hessian matrix of the unknown functions, which include the complex Hessian equations and quotient equations as special cases.

An asymptotic treatment for non-convex fully nonlinear elliptic equations: Global Sobolev and BMO type estimates

2019 ◽  
Vol 21 (07) ◽  
pp. 1850053 ◽  
Author(s):  
J. V. da Silva ◽  
G. C. Ricarte
Keyword(s):  
Elliptic Equations ◽  
A Priori Estimates ◽  
Integrability Condition ◽  
A Priori ◽  
Nonlinear Elliptic Equations ◽  
Borderline Case ◽  
Fully Nonlinear Elliptic Equations ◽  
Fully Nonlinear ◽  
Text Type ◽  
Nonlinear Elliptic

In this paper, we establish global Sobolev a priori estimates for [Formula: see text]-viscosity solutions of fully nonlinear elliptic equations as follows: [Formula: see text] by considering minimal integrability condition on the data, i.e. [Formula: see text] for [Formula: see text] and a regular domain [Formula: see text], and relaxed structural assumptions (weaker than convexity) on the governing operator. Our approach makes use of techniques from geometric tangential analysis, which consists in transporting “fine” regularity estimates from a limiting operator, the Recession profile, associated to [Formula: see text] to the original operator via compactness methods. We devote special attention to the borderline case, i.e. when [Formula: see text]. In such a scenery, we show that solutions admit [Formula: see text] type estimates for their second derivatives.

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