An extrapolation result in the variational setting: improved regularity, compactness, and applications to quasilinear systems
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2023
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866915369735684096 |
|---|---|
| author | Bechtel, Sebastian Veraar, Mark |
| author_facet | Bechtel, Sebastian Veraar, Mark |
| contents | In this paper we consider the variational setting for SPDE on a Gelfand triple $(V, H, V^*)$. Under the standard conditions on a linear coercive pair $(A,B)$, and a symmetry condition on $A$ we manage to extrapolate the classical $L^2$-estimates in time to $L^p$-estimates for some $p>2$ without any further conditions on $(A,B)$. As a consequence we obtain several other a priori regularity results of the paths of the solution.
Under the assumption that $V$ embeds compactly into $H$, we derive a universal compactness result quantifying over all $(A,B)$. As an application of the compactness result we prove global existence of weak solutions to a system of second order quasi-linear equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_01271 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | An extrapolation result in the variational setting: improved regularity, compactness, and applications to quasilinear systems Bechtel, Sebastian Veraar, Mark Probability Analysis of PDEs Classical Analysis and ODEs Functional Analysis Primary: 60H15. Secondary: 35A01, 35B65, 35K59, 35K90, 47H05, 47J35 In this paper we consider the variational setting for SPDE on a Gelfand triple $(V, H, V^*)$. Under the standard conditions on a linear coercive pair $(A,B)$, and a symmetry condition on $A$ we manage to extrapolate the classical $L^2$-estimates in time to $L^p$-estimates for some $p>2$ without any further conditions on $(A,B)$. As a consequence we obtain several other a priori regularity results of the paths of the solution. Under the assumption that $V$ embeds compactly into $H$, we derive a universal compactness result quantifying over all $(A,B)$. As an application of the compactness result we prove global existence of weak solutions to a system of second order quasi-linear equations. |
| title | An extrapolation result in the variational setting: improved regularity, compactness, and applications to quasilinear systems |
| topic | Probability Analysis of PDEs Classical Analysis and ODEs Functional Analysis Primary: 60H15. Secondary: 35A01, 35B65, 35K59, 35K90, 47H05, 47J35 |
| url | https://arxiv.org/abs/2311.01271 |