Monotonicity of solutions of Fully nonlinear uniformly elliptic equations in the half-plane

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:251

Article

Charro, F.²  Montoro, L.¹  Sciunzi, B.¹ 

[1] UNICAL, Dipartimento Matemat, I-87036 Cosenza, Italy

[2] Univ Texas Austin, Dept Math, Austin, TX 78712 USA

关键词: Fully nonlinear;    Uniformly elliptic;    Viscosity solutions;    Monotonicity of solutions;   

DOI  :  10.1016/j.jde.2011.06.005

来源: Elsevier

【 摘 要 】

In this paper we study the monotonicity of positive (or non-negative) viscosity solutions to uniformly elliptic equations F(del u, D(2)u) = f(u) in the half plane, where f is locally Lipschitz continuous (with f(0) >= 0) and zero Dirichlet boundary conditions are imposed. The result is obtained without assuming the u or vertical bar del u vertical bar are bounded. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

Free