Global Gradient Estimates for Nonlinear Elliptic Equations with Vanishing Neumann Data in a Convex Domain

2016 ◽  
Vol 23 (2) ◽  
pp. 337-348
Author(s):  
Fengping Yao
Keyword(s):  
Convex Domain ◽  
Elliptic Equations ◽  
Nonlinear Elliptic Equations ◽  
Gradient Estimates ◽  
Nonlinear Elliptic

scholarly journals Gradient estimates in Orlicz space for nonlinear elliptic equations

2008 ◽  
Vol 255 (8) ◽  
pp. 1851-1873 ◽  
Author(s):  
Sun-Sig Byun ◽  
Fengping Yao ◽  
Shulin Zhou
Keyword(s):  
Orlicz Space ◽  
Elliptic Equations ◽  
Nonlinear Elliptic Equations ◽  
Gradient Estimates ◽  
Nonlinear Elliptic

scholarly journals Gradient estimates and comparison principle for some nonlinear elliptic equations

2015 ◽  
Vol 14 (3) ◽  
pp. 897-922 ◽  
Author(s):  
Maria Francesca Betta ◽  
Rosaria Di Nardo ◽  
Anna Mercaldo ◽  
Adamaria Perrotta
Keyword(s):  
Comparison Principle ◽  
Elliptic Equations ◽  
Nonlinear Elliptic Equations ◽  
Gradient Estimates ◽  
Nonlinear Elliptic

Hölder gradient estimates for fully nonlinear elliptic equations

1988 ◽  
Vol 108 (1-2) ◽  
pp. 57-65 ◽  
Author(s):  
Neil S. Trudinger
Keyword(s):  
Viscosity Solutions ◽  
Elliptic Equations ◽  
Existence Theorems ◽  
Nonlinear Elliptic Equations ◽  
Obstacle Problems ◽  
Gradient Estimates ◽  
Classical Solutions ◽  
Nonlinear Elliptic ◽  
Differential Game Theory ◽  
Special Case

SynopsisIn this paper we prove interior and global Hölder estimates for Lipschitz viscosity solutions of second order, nonlinear, uniformly elliptic equations. The smoothness hypotheses on the operators are more general than previously considered for classical solutions, so that our estimates are also new in this case and readily extend to embrace obstacle problems. In particular Isaac's equations of stochastic differential game theory constitute a special case of our results, and moreover our techniques, in combination with recent existence theorems of Ishii, lead to existence theorems for continuously differentiable viscosity solutions of the uniformly elliptic Isaac's equation.

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