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

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