per il prossimo evento del
ciclo dei Seminari di Analisi, giovedì 20 febbraio alle
17 in Aula Magna, avremo
il piacere di ascoltare Raoní
Cabral Ponciano (UFABC,
Brasile), che
terrà un seminario dal
titolo "Sharp Sobolev and Adams-Trudinger-Moser embeddings for symmetric
functions without boundary conditions on hyperbolic spaces”.
Trovate l'abstract qui sotto.
Il
seminario successivo sarà giovedì 27, con oratore Giorgio Tortone (UniPi). Seguiranno dettagli.
A
presto,
Ilaria
Lucardesi e Luigi Forcella
-----------------------------------
Dear
all,
on Thursday February 20th at 5PM in Aula
Magna, for
the Mathematical Analysis Seminar, we will have the pleasure of listening to Raoní
Cabral Ponciano (UFABC, Brazil). The
title of the talk is
"Sharp Sobolev and Adams-Trudinger-Moser embeddings for symmetric functions
without boundary conditions on hyperbolic spaces". Please find the abstract below.
The following
seminar will be on thursday 27th, with speaker Giorgio Tortone (UniPi). Details will follow.
See
you soon,
Ilaria
Lucardesi and Luigi Forcella
-----------------------------------
Speaker: Raoní Cabral Ponciano (UFABC, Brazil)
Title: Sharp
Sobolev and Adams-Trudinger-Moser embeddings for symmetric functions without boundary conditions on hyperbolic spaces
Abstract: Embedding theorems for symmetric functions without any boundary
conditions have been studied on flat Riemannian manifolds, such as the Euclidean space. However, these theorems have only been established
on hyperbolic spaces for functions with homogeneous Dirichlet conditions. In this presentation, we focus on sharp Sobolev and
Adams–Trudinger–Moser embeddings for radial functions in hyperbolic spaces, considering both bounded and unbounded domains. One of the main features
of our approach is that we do not assume any boundary conditions for symmetric functions on geodesic balls or the entire hyperbolic
space. Our main results establish weighted Sobolev embedding theorems and present Adams-Trudinger-Moser type of embedding theorems. In
particular, a key result is a highly nontrivial comparison between norms of the higher-order covariant derivatives and higher-order derivatives
of the radial functions. Higher-order asymptotic behavior of radial functions on hyperbolic spaces is established to prove our main theorems.
This approach includes novel radial lemmas and decay properties of higher-order radial Sobolev functions defined in hyperbolic
space.