Hessian estimates for equations involving p-Laplacian via a fundamental inequality

2020 ◽  
Vol 370 ◽  
pp. 107212
Author(s):  
Hongjie Dong ◽  
Fa Peng ◽  
Yi Ru-Ya Zhang ◽  
Yuan Zhou
Keyword(s):  
Hessian Estimates

scholarly journals Hessian estimates for convex solutions to quadratic Hessian equation

2019 ◽  
Vol 36 (2) ◽  
pp. 451-454 ◽  
Author(s):  
Matt McGonagle ◽  
Chong Song ◽  
Yu Yuan
Keyword(s):  
Hessian Equation ◽  
Hessian Estimates

Weighted Orlicz regularity estimates for fully nonlinear elliptic equations with asymptotic convexity

2019 ◽  
Vol 21 (04) ◽  
pp. 1850024 ◽  
Author(s):  
Mikyoung Lee
Keyword(s):  
Elliptic Equations ◽  
Nonlinear Operator ◽  
Orlicz Spaces ◽  
Nonlinear Elliptic Equations ◽  
Fully Nonlinear Elliptic Equations ◽  
Fully Nonlinear ◽  
Nonlinear Elliptic ◽  
Regularity Estimates ◽  
Hessian Estimates ◽  
Asymptotic Convexity

We prove interior Hessian estimates in the setting of weighted Orlicz spaces for viscosity solutions of fully nonlinear, uniformly elliptic equations [Formula: see text] under asymptotic assumptions on the nonlinear operator [Formula: see text] The results are further extended to fully nonlinear, asymptotically elliptic equations.

scholarly journals Counterexamples to C2 Boundary Estimates for a Fully Nonlinear Yamabe Problem on Manifolds with Boundary

2012 ◽  
Vol 12 (4) ◽  
Author(s):  
YanYan Li ◽  
Luc Nguyen
Keyword(s):  
Mean Curvature ◽  
A Priori Estimates ◽  
A Priori ◽  
Gradient Estimates ◽  
Manifolds With Boundary ◽  
Fully Nonlinear ◽  
Priori Estimates ◽  
Hessian Estimates ◽  
The Mean ◽  
Boundary Estimates

AbstractOn closed manifolds, gradient and Hessian a priori estimates for fully nonlinear Yamabe problems are known to hold. On manifolds with boundary, gradient estimates are known to hold, while Hessian estimates hold if the prescribed mean curvature is positive. Examples are given here which show that Hessian estimates can fail when the mean curvature is negative.

Hessian estimates for the sigma-2 equationin dimension 3

2009 ◽  
Vol 62 (3) ◽  
pp. 305-321 ◽  
Author(s):  
Micah Warren ◽  
Yu Yuan
Keyword(s):  
Hessian Estimates

scholarly journals Kalman Filter based Newton Extremum Seeking Control for Maximum Gases Production Rates of Anaerobic Digestion Process

2020 ◽  
Vol 49 (4) ◽  
pp. 455-463
Author(s):  
Haoping Wang ◽  
Maobo Hu ◽  
Yang Tian ◽  
Ivan Simeonov ◽  
Lyudmila Kabaivanova ◽  
...  
Keyword(s):  
Kalman Filter ◽  
Anaerobic Digestion ◽  
Extremum Seeking ◽  
Production Rates ◽  
Extremum Seeking Control ◽  
Filtering Algorithm ◽  
Anaerobic Digestion Process ◽  
Digestion Process ◽  
Input And Output ◽  
Hessian Estimates

This paper proposes a Kalman filter (KF) based Newton extremum seeking control (NESC) to maximize production rates of hydrogen and methane in anaerobic digestion process. The Kalman filtering algorithm is used to obtain more accurate gradient and Hessian estimates which makes possible to increase the convergence speed to the extremum and to eliminate input and output steady-state oscillations. The simulation examples demonstrate the performances of the proposed approach.

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