Gradient estimates for singular fully nonlinear elliptic equations

被引：2

作者：

Lieberman, Gary M. ^{[1
]}

机构：

[1] Iowa State Univ, Dept Math, Ames, IA 50011 USA

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2015年 / 119卷

关键词：

Singular differential equations; Nonlinear partial differential equations; a priori estimates; CONORMAL DERIVATIVE PROBLEM; REGULARITY;

D O I：

10.1016/j.na.2014.10.031

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study a class of singular fully nonlinear elliptic equations under suitable natural conditions, with the model equation being Delta u + b(gamma . Du)/d - u + c vertical bar Du vertical bar(2) = f for Lipschitz functions b > 0, c and f, where d denotes distance to the boundary of the domain and gamma is a suitable extension of the interior unit normal. We show that such equations have a unique, globally C-1 solution (without any a priori prescription of boundary data). (C) 2014 Elsevier Ltd. All rights reserved.

引用

页码：382 / 397

页数：16

共 50 条

[21] Gradient estimate for solutions of nonlinear singular elliptic equations below the duality exponent
Cirmi, G. R.
D'Asero, S.
Leonardi, S.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2018, 41 (01) : 261 - 269
[22] Weighted gradient estimates for general nonlinear elliptic equations involving measure data
Zhang, Junjie
Zheng, Shenzhou
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2020, 488 (01)
[23] Estimates for fully anisotropic elliptic equations with a zero order term
Alberico, A.
di Blasio, G.
Feo, F.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2019, 181 : 249 - 264
[24] Local Gradient Estimates for Degenerate Elliptic Equations
Luan Hoang
Truyen Nguyen
Tuoc Phan
ADVANCED NONLINEAR STUDIES, 2016, 16 (03) : 479 - 489
[25] Gradient estimates for elliptic equations with measurable nonlinearities
Kim, Youchan
JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2018, 114 : 118 - 145
[26] Second order estimates for Hessian type fully nonlinear elliptic equations on Riemannian manifolds
Guan, Bo
Jiao, Heming
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2015, 54 (03) : 2693 - 2712
[27] CURVATURE ESTIMATES FOR A CLASS OF FULLY NONLINEAR ELLIPTIC EQUATIONS WITH GENERAL RIGHT HAND SIDES
Zhou, Jundong
BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY, 2024, 61 (02) : 355 - 379
[28] Interior gradient estimates for quasilinear elliptic equations
Truyen Nguyen
Tuoc Phan
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2016, 55 (03)
[29] Global gradient estimates for very singular quasilinear elliptic equations with non-divergence data
Minh-Phuong Tran
Thanh-Nhan Nguyen
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2022, 214
[30] C1,α regularity for fully nonlinear elliptic equations with superlinear growth in the gradient
Nornberg, Gabrielle
JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2019, 128 : 297 - 329

← 1 2 3 4 5 →