Fully nonlinear Hamilton-Jacobi equations of degenerate type

被引：1
|
作者：
Jesus, David [1 ]
Pimentel, Edgard A. [1 ,2 ]
Urbano, Jose Miguel [1 ,3 ]
机构：
[1] Univ Coimbra, Dept Math, CMUC, P-3001501 Coimbra, Portugal
[2] Pontifical Catholic Univ Rio De Janeiro PUC Rio, BR-22451900 Rio De Janeiro, RJ, Brazil
[3] King Abdullah Univ Sci & Technol KAUST, Comp Elect & Math Sci & Engn Div CEMSE, Thuwal 239556900, Saudi Arabia
来源：
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2023年 / 227卷
关键词：
Degenerate elliptic operators; Hamilton-Jacobi equation; Lipschitz regularity; Two-phase free boundary problems; VISCOSITY SOLUTIONS; ELLIPTIC-EQUATIONS; REGULARITY; EXISTENCE; PROOF;
D O I：
10.1016/j.na.2022.113181
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We examine Hamilton-Jacobi equations driven by fully nonlinear degenerate elliptic operators in the presence of superlinear Hamiltonians. By exploring the Ishii-Jensen inequality, we prove that viscosity solutions are locally Lipschitz-continuous, with estimates depending on the structural conditions of the problem. We close the paper with an application of our findings to a two-phase free boundary problem. (c) 2022 Elsevier Ltd. All rights reserved.
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页数：15
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