scholarly journals Second order estimates for Hessian type fully nonlinear elliptic equations on Riemannian manifolds

2015 ◽  
Vol 54 (3) ◽  
pp. 2693-2712 ◽  
Author(s):  
Bo Guan ◽  
Heming Jiao
Keyword(s):  
Riemannian Manifolds ◽  
Elliptic Equations ◽  
Nonlinear Elliptic Equations ◽  
Second Order ◽  
Fully Nonlinear Elliptic Equations ◽  
Fully Nonlinear ◽  
Nonlinear Elliptic

scholarly journals On the existence of Wp2 solutions for fully nonlinear elliptic equations under either relaxed or no convexity assumptions

2017 ◽  
Vol 19 (06) ◽  
pp. 1750009 ◽  
Author(s):  
N. V. Krylov
Keyword(s):  
Elliptic Equations ◽  
Existence Of Solutions ◽  
Nonlinear Elliptic Equations ◽  
Second Order ◽  
Fully Nonlinear Elliptic Equations ◽  
Sobolev Classes ◽  
Fully Nonlinear ◽  
Nonlinear Elliptic ◽  
Convexity Assumptions ◽  
Second Order Equations

We establish the existence of solutions of fully nonlinear elliptic second-order equations like [Formula: see text] in smooth domains without requiring [Formula: see text] to be convex or concave with respect to the second-order derivatives. Apart from ellipticity nothing is required of [Formula: see text] at points at which [Formula: see text], where [Formula: see text] is any given constant. For large [Formula: see text] some kind of relaxed convexity assumption with respect to [Formula: see text] mixed with a VMO condition with respect to [Formula: see text] are still imposed. The solutions are sought in Sobolev classes. We also establish the solvability without almost any conditions on [Formula: see text], apart from ellipticity, but of a “cut-off” version of the equation [Formula: see text].

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.

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