Principal eigenvalues and the Dirichlet problem for fully nonlinear elliptic operators
نویسندگان
چکیده
We study uniformly elliptic fully nonlinear equations of the type F (D2u,Du, u, x) = f(x). We show that convex positively 1-homogeneous operators possess two principal eigenvalues and eigenfunctions, and study these objects ; we obtain existence and uniqueness results for non-proper operators whose principal eigenvalues (in some cases, only one of them) are positive ; finally, we obtain an existence result for non-proper Isaac’s equations. 2000 Mathematics Subject Classification : 35J60, 35J65, 35P30.
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تاریخ انتشار 2010