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- W4293455803 abstract "We study fully nonlinear elliptic equations such as [ F(D^2u) = u^p, quad p>1, ] in $R^n$ or 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-V'eron cite{B} as well as Cutri and Leoni cite{CL}, 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." @default.
- W4293455803 created "2022-08-29" @default.
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- W4293455803 date "2010-01-25" @default.
- W4293455803 modified "2023-10-08" @default.
- W4293455803 title "Sharp Liouville results for fully nonlinear equations with power-growth nonlinearities" @default.
- W4293455803 doi "https://doi.org/10.48550/arxiv.1001.4489" @default.
- W4293455803 hasPublicationYear "2010" @default.
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