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math.AP2022
Liouville-type theorems for the Lane-Emden equation in the half-space and cones
Louis Dupaigne, Alberto Farina, Troy Petitt
We prove that 0 the only classical solution of the Lane-Emden equation in the half-space which is stable outside a compact set. We also consider weak solutions and the case of gene…
math.AP2022
An inhomogeneous porous medium equation with large data: well-posedness
Matteo Muratori, Troy Petitt
We study solutions of a Euclidean weighted porous medium equation when the weight behaves at spacial infinity like , for , and is allowed to be singular at th…