07-48

Rotationally symmetric classical solutions to the Dirichlet problem for Willmore surfaces

by Dall\'Acqua, A.; Deckelnick, K.; Grunau, H.-Ch.

 

Preprint series: 07-48, Preprints

The paper is published: Erschienen unter dem Titel

MSC:
53C42 Immersions (minimal, prescribed curvature, tight, etc.), See also {49Q05, 49Q10, 53A10, 57R40, 57R42}
35J65 Nonlinear boundary value problems for linear elliptic PDE; boundary value problems for nonlinear elliptic PDE
49K20 Problems involving partial differential equations

 

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

Keywords: rotationally symmetric Willmore surfaces, hyperbolic half plane


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