On the limiting behaviour of some nonlocal seminorms: a new phenomenon

Federico Buseghin; Nicola Garofalo; Giulio Tralli

doi:10.2422/2036-2145.202005_014

On the limiting behaviour of some nonlocal seminorms: a new phenomenon

Federico Buseghin, Nicola Garofalo, Giulio Tralli

Department of Mathematical Sciences

Università di Padova

Research output: Contribution to journal › Article › peer-review

17 Citations (SciVal)

Abstract

In this note we study the behaviour as s → 0+ of some semigroup based Besov seminorms associated with a non-symmetric and hypoelliptic diffusion with a drift. Our results generalise a previous one of Maz'ya and Shaposhnikova for the classical fractional Sobolev spaces W s;p, and they also underscore a new phenomenon caused by the presence of the drift.

Original language	English
Pages (from-to)	837-875
Number of pages	39
Journal	Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
Volume	23
Issue number	2
DOIs	https://doi.org/10.2422/2036-2145.202005_014
Publication status	Published - 23 Jun 2022

ASJC Scopus subject areas

Theoretical Computer Science
Mathematics (miscellaneous)

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10.2422/2036-2145.202005_014

https://arxiv.org/abs/2004.01303

Cite this

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AU - Garofalo, Nicola

AU - Tralli, Giulio

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AB - In this note we study the behaviour as s → 0+ of some semigroup based Besov seminorms associated with a non-symmetric and hypoelliptic diffusion with a drift. Our results generalise a previous one of Maz'ya and Shaposhnikova for the classical fractional Sobolev spaces W s;p, and they also underscore a new phenomenon caused by the presence of the drift.

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On the limiting behaviour of some nonlocal seminorms: a new phenomenon

Abstract

ASJC Scopus subject areas

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