Garcke, Harald 
; Menzel, Julia ; Pluda, Alessandra
Alternative Links zum Volltext:DOIVerlag
| Dokumentenart: | Artikel |
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| Titel eines Journals oder einer Zeitschrift: | Journal of Differential Equations |
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| Verlag: | ACADEMIC PRESS INC ELSEVIER SCIENCE |
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| Ort der Veröffentlichung: | SAN DIEGO |
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| Band: | 266 |
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| Nummer des Zeitschriftenheftes oder des Kapitels: | 4 |
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| Seitenbereich: | S. 2019-2051 |
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| Datum: | 2019 |
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| Institutionen: | Mathematik |
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| Identifikationsnummer: | | Wert | Typ |
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| 10.1016/j.jde.2018.08.019 | DOI |
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| Stichwörter / Keywords: | STRAIGHTENING FLOW; ELASTIC CURVES; EXISTENCE; L-2-FLOW; Geometric evolution equations; Willmore flow; Networks; Parabolic systems of fourth order; Junctions |
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| Dewey-Dezimal-Klassifikation: | 500 Naturwissenschaften und Mathematik > 510 Mathematik |
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| Status: | Veröffentlicht |
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| Begutachtet: | Ja, diese Version wurde begutachtet |
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| An der Universität Regensburg entstanden: | Ja |
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| Dokumenten-ID: | 48996 |
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Zusammenfassung
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 ...
Zusammenfassung
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.
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