Details
| Original language | English |
|---|---|
| Pages (from-to) | 288-325 |
| Number of pages | 38 |
| Journal | Journal of Differential Equations |
| Volume | 269 |
| Issue number | 1 |
| Early online date | 31 Dec 2019 |
| Publication status | Published - 15 Jun 2020 |
Abstract
In this article we study the class of right-invariant, fractional order Sobolev-type metrics on groups of diffeomorphisms of a compact manifold M. Our main result concerns well-posedness properties for the corresponding Euler-Arnold equations, also called the EPDiff equations, which are of importance in mathematical physics and in the field of shape analysis and template registration. Depending on the order of the metric, we will prove both local and global well-posedness results for these equations. As a result of our analysis we will also obtain new commutator estimates for elliptic pseudo-differential operators.
Keywords
- Diffeomorphism groups, EPDiff equation, Sobolev metrics of fractional order
ASJC Scopus subject areas
- Mathematics(all)
- Analysis
- Mathematics(all)
- Applied Mathematics
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In: Journal of Differential Equations, Vol. 269, No. 1, 15.06.2020, p. 288-325.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Well-posedness of the EPDiff equation with a pseudo-differential inertia operator
AU - Bauer, Michael
AU - Bruveris, Martins
AU - Cismas, Emanuel
AU - Escher, Joachim
AU - Kolev, Boris
N1 - Funding information: M. Bauer was partially supported by NSF-grant 1912037 (collaborative research in connection with NSF-grant 1912030) and E. Cismas was partially supported by CNCS UEFISCDI, project number PN-III-P4-ID-PCE-2016-0778.
PY - 2020/6/15
Y1 - 2020/6/15
N2 - In this article we study the class of right-invariant, fractional order Sobolev-type metrics on groups of diffeomorphisms of a compact manifold M. Our main result concerns well-posedness properties for the corresponding Euler-Arnold equations, also called the EPDiff equations, which are of importance in mathematical physics and in the field of shape analysis and template registration. Depending on the order of the metric, we will prove both local and global well-posedness results for these equations. As a result of our analysis we will also obtain new commutator estimates for elliptic pseudo-differential operators.
AB - In this article we study the class of right-invariant, fractional order Sobolev-type metrics on groups of diffeomorphisms of a compact manifold M. Our main result concerns well-posedness properties for the corresponding Euler-Arnold equations, also called the EPDiff equations, which are of importance in mathematical physics and in the field of shape analysis and template registration. Depending on the order of the metric, we will prove both local and global well-posedness results for these equations. As a result of our analysis we will also obtain new commutator estimates for elliptic pseudo-differential operators.
KW - Diffeomorphism groups
KW - EPDiff equation
KW - Sobolev metrics of fractional order
UR - http://www.scopus.com/inward/record.url?scp=85077170450&partnerID=8YFLogxK
U2 - 10.1016/j.jde.2019.12.008
DO - 10.1016/j.jde.2019.12.008
M3 - Article
AN - SCOPUS:85077170450
VL - 269
SP - 288
EP - 325
JO - Journal of Differential Equations
JF - Journal of Differential Equations
SN - 0022-0396
IS - 1
ER -