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: email@example.com
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
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