Garcke, Harald and Menzel, Julia and Pluda, Alessandra (2019) Willmore flow of planar networks. JOURNAL OF DIFFERENTIAL EQUATIONS, 266 (4). pp. 2019-2051. ISSN 0022-0396, 1090-2732
Full text not available from this repository. (Request a copy)Abstract
Geometric gradient flows for elastic energies of Willmore type play an important role in mathematics and in many applications. The evolution of elastic curves has been studied in detail both for closed as well as for open curves. Although elastic flows for networks also have many interesting features, they have not been studied so far from the point of view of mathematical analysis. So far it was not even clear what are appropriate boundary conditions at junctions. In this paper we give a well-posedness result for Willmore flow of networks in different geometric settings and hence lay a foundation for further mathematical analysis. A main point in the proof is to check whether different proposed boundary conditions lead to a well posed problem. In this context one has to check the Lopatinskii-Shapiro condition in order to apply the Solonnikov theory for linear parabolic systems in Holder spaces which is needed in a fixed point argument. We also show that the solution we get is unique in a purely geometric sense. (C) 2018 Elsevier Inc. All rights reserved.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | STRAIGHTENING FLOW; ELASTIC CURVES; EXISTENCE; L-2-FLOW; Geometric evolution equations; Willmore flow; Networks; Parabolic systems of fourth order; Junctions |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 17 Apr 2020 11:44 |
| Last Modified: | 17 Apr 2020 11:44 |
| URI: | https://pred.uni-regensburg.de/id/eprint/27566 |
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