Comparison principle for unbounded viscosity solutions of degenerate elliptic PDEs with gradient superlinear terms

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:381

Article

Koike, Shigeaki²  Ley, Olivier¹ 

[1] INSA Rennes, IRMAR, F-35708 Rennes, France

[2] Saitama Univ, Dept Math, Sakura Ku, Saitama 3388570, Japan

关键词: Viscosity solution;    Comparison principle;    Nonconvex Hamiltonians;    Growth conditions;    Systems of PDE;   

DOI  :  10.1016/j.jmaa.2011.03.009

来源: Elsevier

【 摘 要 】

We are concerned with fully nonlinear possibly degenerate elliptic partial differential equations (PDEs) with superlinear terms with respect to Du. We prove several comparison principles among viscosity solutions which may be unbounded under some polynomial-type growth conditions. Our main result applies to PDEs with convex superlinear terms but we also obtain some results in nonconvex cases. Applications to monotone systems of PDEs are given. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

Free