3 papers
math.AP2025
On the Heat equation involving a Grushin operator in Marcinkiewcz spaces
Alessia E. Kogoj, Maria E. Lima, Arlúcio Viana
In this work, we give sufficient conditions for the existence and uniqueness of the heat equation involving the operator $$ Î_{\mathcal{G}}=\dfrac{1}{2}\left(Î_{x}+|x|^2Î_{y}\ri…
math.AP2025
Asymptotic average solutions for second order hypoelliptic PDEs
Alessia E. Kogoj
Following an analogous procedure with that used in \cite{kogoj_lanconelli_pizzetti}, in turn inspired by a 1909 paper by Pizzetti \cite{pizzetti}, we introduce the notion of {\it a…
math.AP2025
One-side Liouville Theorem for hypoelliptic Ornstein--Uhlenbeck operators having drifts with imaginary spectrum
Alessia E. Kogoj, Ermanno Lanconelli, Giulio Tralli
We prove the Liouville theorem for \emph{non-negative} solutions to (possibly degenerate) Ornstein-Uhlenbeck equations whose linear drift has imaginary spectrum. This provides an a…