scholarly journals Regularity estimates for fully nonlinear elliptic PDEs with general Hamiltonian terms and unbounded ingredients

2021 ◽  
Vol 60 (6) ◽  
Author(s):  
João Vitor da Silva ◽  
Gabrielle Nornberg
Keyword(s):  
Elliptic Pdes ◽  
Fully Nonlinear ◽  
Nonlinear Elliptic ◽  
Regularity 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 Borderline regularity for fully nonlinear equations in Dini domains

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Karthik Adimurthi ◽  
Agnid Banerjee
Keyword(s):  
Nonlinear Equations ◽  
Elliptic Equations ◽  
Nonlinear Elliptic Equations ◽  
Fully Nonlinear Elliptic Equations ◽  
Fully Nonlinear Equations ◽  
Fully Nonlinear ◽  
Nonlinear Elliptic ◽  
Regularity Estimates ◽  
Compactness Arguments ◽  
Gradient Regularity

AbstractIn this paper, we prove borderline gradient continuity of viscosity solutions to fully nonlinear elliptic equations at the boundary of a C^{1,\mathrm{Dini}}-domain. Our main result constitutes the boundary analogue of the borderline interior gradient regularity estimates established by P. Daskalopoulos, T. Kuusi and G. Mingione. We however mention that, differently from the approach used there which is based on W^{1,q} estimates, our proof is slightly more geometric and is based on compactness arguments inspired by the techniques in the fundamental works of Luis Caffarelli.

Two-grid IPDG discretization scheme for nonlinear elliptic PDEs

2020 ◽  
pp. 105587
Author(s):  
Liuqiang Zhong ◽  
Liangliang Zhou ◽  
Chunmei Liu ◽  
Jie Peng
Keyword(s):  
Elliptic Pdes ◽  
Discretization Scheme ◽  
Nonlinear Elliptic
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