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Uniqueness for the Homogeneous Dirichlet Willmore boundary value problem

by Dall'Acqua, A..

Series: 2011-06, Preprints

35G25 Initial value problems for nonlinear higher-order equations

We prove that a Willmore surface which has its boundary on a strict star-shaped two-dimensional domain and which intersects the plane of the domain with a zero angle, along the boundary, is necessarily a piece of the plane.

Willmore surfaces, Dirichlet boundary conditions, Pohozaev identity, conformal Gauss map