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Classical solutions to the Dirichlet problem for Willmore surfaces of revolution

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Veröffentlicht/Copyright: 8. Dezember 2008
Advances in Calculus of Variations
Aus der Zeitschrift Band 1 Heft 4

Abstract

We consider the Willmore equation with Dirichlet boundary conditions for a surface of revolution obtained by rotating the graph of a positive smooth even function. We show existence of a regular solution by minimisation. Instead of minimising the Willmore functional we reformulate the problem in the hyperbolic half plane and we minimise the corresponding “hyperbolic Willmore functional”.

Keywords.: Dirichlet boundary conditions; Willmore surfaces of revolution
Received: 2007-12-13
Revised: 2008-08-04
Published Online: 2008-12-08
Published in Print: 2008-December

© de Gruyter 2008

Artikel in diesem Heft

  1. On the behaviour of free H-surfaces near singular points of the support surface
  2. Classical solutions to the Dirichlet problem for Willmore surfaces of revolution
  3. A discrete variational principle for rate-independent evolution
https://doi.org/10.1515/ACV.2008.016
Schlagwörter für diesen Artikel
Dirichlet boundary conditions; Willmore surfaces of revolution

Artikel in diesem Heft

  1. On the behaviour of free H-surfaces near singular points of the support surface
  2. Classical solutions to the Dirichlet problem for Willmore surfaces of revolution
  3. A discrete variational principle for rate-independent evolution
Heruntergeladen am 12.4.2026 von https://www.degruyterbrill.com/document/doi/10.1515/ACV.2008.016/html
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