6 papers · 1 filter
Preservation of F-convexity under the heat flow
Kazuhiro Ishige, Troy Petitt, Paolo Salani
We introduce the notion of F-convexity as a general extension of power convexity. We characterize the F-convexities preserved under the heat flow in the n-dimensional Euclidean spa…
Rigidity of weighted manifolds via classification results for semilinear equations
Giulio Ciraolo, Alberto Farina, Troy Petitt
We study model semilinear equations on complete and non-compact weighted Riemannian manifolds with non-negative Bakry-Émery Ricci curvature. Our main goal is to classify positive s…
A porous medium equation with rough weights: sharp Widder theory
Gabriele Grillo, Matteo Muratori, Troy Petitt +1
We establish an optimal \emph{Widder theory} for a weighted porous medium equation with rough and inhomogeneous density that may be singular at a point and tends to zero at spatial…
An inhomogeneous porous medium equation with non-integrable data: asymptotics
Matteo Muratori, Troy Petitt, Fernando Quirós
We investigate the asymptotic behavior as of solutions to a weighted porous medium equation in , whose weight behaves at spatial infinity like…
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…
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…