Viscosity solutions to the degenerate oblique derivative problem for fully nonlinear elliptic equations

2005 ◽  
Vol 278 (7-8) ◽  
pp. 888-903 ◽  
Author(s):  
P. Popivanov ◽  
N. Kutev
Keyword(s):  
Viscosity Solutions ◽  
Elliptic Equations ◽  
Nonlinear Elliptic Equations ◽  
Oblique Derivative Problem ◽  
Fully Nonlinear Elliptic Equations ◽  
Fully Nonlinear ◽  
Derivative Problem ◽  
Nonlinear Elliptic

scholarly journals On the W 2p Estimate for Oblique Derivative Problem in Lipschitz Domains

2020 ◽  
Author(s):  
Hongjie Dong ◽  
Zongyuan Li
Keyword(s):  
Boundary Condition ◽  
Elliptic Equations ◽  
Nonlinear Elliptic Equations ◽  
Divergence Form ◽  
Lipschitz Domains ◽  
Oblique Derivative Problem ◽  
Fully Nonlinear Elliptic Equations ◽  
Fully Nonlinear ◽  
Nonlinear Elliptic ◽  
Lipschitz Constants

Abstract The aim of this paper is to establish $W^2_p$ estimate for non-divergence form 2nd-order elliptic equations with the oblique derivative boundary condition in domains with small Lipschitz constants. Our result generalizes those in [ 16] and [ 17], which work for $C^{1,\alpha }$ domains with $\alpha> 1-1/p$. As an application, we also obtain a solvability result. An extension to fully nonlinear elliptic equations with the oblique derivative boundary condition is also discussed.

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