C1,α Regularity for Degenerate Fully Nonlinear Elliptic Equations with Neumann Boundary Conditions

被引：0
作者：
Agnid Banerjee
Ram Baran Verma
机构：
[1] Tata Institute of Fundamental Research,
[2] Centre For Applicable Mathematics,undefined
来源：
Potential Analysis | 2022年 / 57卷
关键词：
Pucci’s extremal operator; Degenerate elliptic; Viscosity solutions; Regularity; Primary 35J60; 35D40;
D O I：
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学科分类号：
摘要：
In this paper, we establish C1,α regularity up to the boundary for a class of degenerate fully nonlinear elliptic equations with Neumann boundary conditions. Our main result Theorem 2.1 constitutes the boundary analogue of the interior C1,α regularity result established in Imbert and Silvestre (Adv. Math. 233: 196–206, 2013) for equations with similar structural assumptions. The proof of our main result is achieved via compactness arguments combined with new boundary Hölder estimates for equations which are uniformly elliptic when the gradient is either small or large.
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页码：327 / 365
页数：38
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共 46 条
[11]  
Teixeira E(2014)C1,β regularity for Dirichlet problems associated to fully nonlinear degenerate elliptic equations ESAIM Control Optim. Calc. Var. 20 1009-1024
[12]  
Arkhipova AA(1997)Nondivergent elliptic equations on manifolds with nonnegative curvature Comm. Pure Appl. Math. 50 623-665
[13]  
Uraltseva NN(1989)Interior a priori estimates for solutions of fully nonlinear equations Ann. Math. 130 189-213
[14]  
Barles G(1979)Further regulrity for the Signorini problem Comm. Partial Differ. Equ. 4 1067-1075
[15]  
Banerjee A(2014)Regularity results for very degenerate elliptic equations J. Math. Pures. Appl. 111 94-117
[16]  
Kawohl B(1990)Viscosity solutions of fully nonlinear second-order elliptic partial differential equations J. Differ. Equ. 83 26-78
[17]  
Banerjee A(2013)C1,α regularity of solutions of some degenerate fully nonlinear elliptic equations Adv. Math. 233 196-206
[18]  
Lewis J(2016)Estimates on elliptic equations that hold only where the gradient is large J. Eur. Math. Soc. 18 1321-1338
[19]  
Birindelli I(2018)Regularity for fully nonlinear elliptic equations with oblique boundary conditions Arch. Rational Mech. Anal. 228 923-967
[20]  
Demengel F(2015)Harnack inequality for degenerate and singular elliptic equations with unbounded drift J. Differ. Equ. 258 1577-1591
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