Year: 2011
Type: article
Abstract: We study fully nonlinear elliptic equations such asor in exterior domains, where F is any uniformly elliptic, positively homogeneous operator.We show that there exists a critical exponent, depending on the homogeneity of the fundamental solution of F, that sharply characterizes the range of p > 1 for which there exist positive supersolutions or solutions in any exterior domain.Our result generalizes theorems of Bidaut-Véron [6] as well as Cutri and Leoni [11], who found critical exponents for supersolutions in the whole space R n , in case -F is Laplace's operator and Pucci's operator, respectively.The arguments we present are new and rely only on the scaling properties of the equation and the maximum principle.
Authors: Scott N. Armstrong, Boyan Sirakov
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W1840515818