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Planar Regularity Structures.

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Title: Planar Regularity Structures.
Authors: Rahm, Ludwig1 (AUTHOR) ludwig.rahm@ntnu.no
Source: Foundations of Computational Mathematics. Jun2026, Vol. 26 Issue 3, p1269-1319. 51p.
Subjects: Homogeneous spaces, Stochastic partial differential equations, Ordinary differential equations
Abstract: Branched rough paths, used to solve ODEs on R , have been generalised in two different directions. In one direction, there are regularity structures aimed at solving SPDEs on Euclidean spaces. In the other direction, there are planarly branched rough paths to solve ODEs on homogeneous spaces. This paper combines these two directions to construct planar regularity structures, for (S)PDEs on homogeneous spaces. [ABSTRACT FROM AUTHOR]
Copyright of Foundations of Computational Mathematics is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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DbLabel: Engineering Source
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  Data: Branched rough paths, used to solve ODEs on R , have been generalised in two different directions. In one direction, there are regularity structures aimed at solving SPDEs on Euclidean spaces. In the other direction, there are planarly branched rough paths to solve ODEs on homogeneous spaces. This paper combines these two directions to construct planar regularity structures, for (S)PDEs on homogeneous spaces. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Foundations of Computational Mathematics is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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      – SubjectFull: Homogeneous spaces
        Type: general
      – SubjectFull: Stochastic partial differential equations
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      – SubjectFull: Ordinary differential equations
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              Text: Jun2026
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