Volume 27, 2023
|Page(s)||136 - 155|
|Published online||20 January 2023|
A Sobolev rough path extension theorem via regularity structures
1 Shanghai Tech University,
2 Universität Mannheim, Mannheim, Germany
3 Eidgenössische Technische Hochschule Zürich, Zurich, Switzerland
* Corresponding author: firstname.lastname@example.org
Accepted: 9 November 2022
We show that every ℝd-valued Sobolev path with regularity a and integrability p can be lifted to a Sobolev rough path provided 1/2 > α > 1/p> ⋁ 1/3. The novelty of our approach is its use of ideas underlying Hairer’s reconstruction theorem generalized to a framework allowing for Sobolev models and Sobolev modelled distributions. Moreover, we show that the corresponding lifting map is locally Lipschitz continuous with respect to the inhomogeneous Sobolev metric.
Mathematics Subject Classification: 60L20 / 60L30
Key words: Fractional Sobolev space / Lyons-Victoir extension theorem / reconstruction theorem / regularity structures / rough path
© The authors. Published by EDP Sciences, SMAI 2023
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.