THE DIRICHLET PROBLEM FOR FULLY NONLINEAR ELLIPTIC EQUATIONS NON-DEGENERATE IN A FIXED DIRECTION

被引：8

作者：

Mannucci, Paola ^{[1
]}

机构：

[1] Univ Padua, Dipartimento Matemat, I-35121 Padua, Italy

来源：

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS | 2014年 / 13卷 / 01期

关键词：

Viscosity solution; comparison principle; degenerate elliptic equation; Dirichlet problem; subelliptic equation; Pucci's operators; Carnot groups; PARTIAL-DIFFERENTIAL EQUATIONS; VISCOSITY SOLUTIONS; HEISENBERG-GROUP; MAXIMUM PRINCIPLE; VECTOR-FIELDS;

D O I：

10.3934/cpaa.2014.13.119

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove a comparison principle for viscosity solutions of a fully nonlinear equation satisfying a condition of non-degeneracy in a fixed direction. We apply these results to prove that a continuous solution of the corresponding Dirichlet problem exists. To obtain the existence of barrier functions and well-posedness, we find suitable explicit assumptions on the domain and on the ellipticity constants of the operator.

引用

页码：119 / 133

页数：15

共 50 条

[1] On the Dirichlet problem for non-totally degenerate fully nonlinear elliptic equations
Bardi, Martino
Mannucci, Paola
COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2006, 5 (04) : 709 - 731
[2] The Dirichlet problem for fully nonlinear degenerate elliptic equations with a singular nonlinearity
Birindelli, Isabeau
Galise, Giulio
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2019, 58 (05)
[3] The Dirichlet problem for fully nonlinear degenerate elliptic equations with a singular nonlinearity
Isabeau Birindelli
Giulio Galise
Calculus of Variations and Partial Differential Equations, 2019, 58
[4] THE DIRICHLET PROBLEM FOR NONLINEAR DEGENERATE ELLIPTIC EQUATIONS
王传芳
Science Bulletin, 1985, (03) : 422 - 423
[5] On the Dirichlet problem for a class of nonlinear degenerate elliptic equations
Cavalheiro, Albo Carlos
CONTRIBUTIONS TO MATHEMATICS, 2020, 1 : 35 - 44
[6] On the Dirichlet problem for a class of fully nonlinear elliptic equations
Yuan, Rirong
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2021, 60 (05)
[7] Regularity of the Dirichlet Problem for the Non-degenerate Complex Quotient Equations
Zhang, Qiqi
INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2021, 2021 (23) : 17673 - 17694
[8] On the Dirichlet problem for a class of fully nonlinear elliptic equations
Rirong Yuan
Calculus of Variations and Partial Differential Equations, 2021, 60
[9] DIRICHLET PROBLEM FOR DEGENERATE ELLIPTIC EQUATIONS
FRIEDMAN, A
PINSKY, MA
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1973, 186 (459) : 359 - 383
[10] The Dirichlet problem for fully nonlinear elliptic equations on Riemannian manifolds
Guan, Bo
ADVANCES IN MATHEMATICS, 2023, 415

← 1 2 3 4 5 →