Principal eigenvalues and an anti-maximum principle for homogeneous fully nonlinear elliptic equations

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:246

Article

Armstrong, Scott N.

关键词: Fully nonlinear elliptic equation;    Principal eigenvalue;    Dirichlet problem;    Anti-maximum principle;   

DOI  :  10.1016/j.jde.2008.10.026

来源: Elsevier

【 摘 要 】

We study the fully nonlinear elliptic equation F(D(2)u, Du, u, x) = f (0.1) in a smooth bounded domain Omega, under the assumption that the nonlinearity F is uniformly elliptic and positively homogeneous. Recently, it has been shown that such operators have two principal half eigenvalues, and that the corresponding Dirichlet problem possesses solutions, if both of the principal eigenvalues are positive. In this paper, we prove the existence of solutions of the Dirichlet problem if both principal eigenvalues are negative, provided the second eigenvalue is positive, and generalize the anti-maximum principle of Clement and Peletier [P. Clement, LA. Peletier, An anti-maximum principle for second-order elliptic operators, J. Differential Equations 34 (2) (1979) 218-229] to homogeneous, fully nonlinear operators. (C) 2008 Elsevier Inc. All rights reserved.

【 授权许可】

Free