Calculus of Variations and Geometric Measure Theory
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H. Olbermann

On a $Γ$-limit of Willmore functionals with additional curvature penalization term

created by olbermann on 23 Jul 2019

[BibTeX]

preprint

Inserted: 23 jul 2019

Year: 2018

ArXiv: 1807.10701 PDF

Abstract:

We consider the Willmore functional on graphs, with an additional penalization of the area where the curvature is non-zero. Interpreting the penalization parameter as a Lagrange multiplier, this corresponds to the Willmore functional with a constraint on the area where the graph is flat. Sending the penalization parameter to $\infty$ and rescaling suitably, we derive the limit functional in the sense of $\Gamma$-convergence.

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