Corpus ID: 236469125

On the Liouville property for fully nonlinear equations with superlinear first-order terms

@inproceedings{Cirant2021OnTL,
  title={On the Liouville property for fully nonlinear equations with superlinear first-order terms},
  author={Marco Cirant and Alessandro Goffi},
  year={2021}
}
We consider in this note one-side Liouville properties for viscosity solutions of various fully nonlinear uniformly elliptic inequalities, whose prototype is F (x,Du) ≥ Hi(x, u,Du) in R , where Hi has superlinear growth in the gradient variable. After a brief survey on the existing literature, we discuss the validity or the failure of the Liouville property in the model cases H1(u,Du) = u + |Du| , H2(u,Du) = u|Du| and H3(x,Du) = ±u|Du| − b(x) ·Du, where q ≥ 0, γ > 1 and b is a suitable velocity… Expand
Liouville results for fully nonlinear equations modeled on H\"ormander vector fields: II. Carnot groups and Grushin geometries
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